This is done by ear, so apologies if not 100% accurate. Sounds ok to me though.....
Just a note , on the chorus, the notes on the riff coincide with the lyrics, so play 
that note on that lyric, just to make it a bit easier for coordination.
Any improvements, let me know thelibertine1986@hotmail.co.uk

Power chords for verses (palm muted!!!)

  G    C    Em

E|-|  |-|  |-|
B|-|  |-|  |-|
G|-|  |-|  |-|
D|-|  |5|  |-|
A|5|  |3|  |2|
E|3|  |-|  |0|

Intro - Play through twice

GI

E|-----------------------------------------------|
B|----12-12----12------12---12----12-13-13-12----|
G|-14-------14------14---------14-------------14-|
D|-----------------------------------------------|
A|-----------------------------------------------|
E|-----------------------------------------------|

GII

E|---------------------------------|
B|---------------------------------|
G|---------------------------------|
D|-5-5-5-5-5---5-5---5-5-5-5-5-5-5-|
A|-5-5-5-5-5---5-5---5-5-5-5-5-5-5-|
E|-3-3-3-3-3---3-3---3-3-3-3-3-3-3-|

GI

E|-----------------------------------------------|
B|----12-12----12------12---12----12-15-15-12----|
G|-14-------14------14---------14-------------14-|
D|-----------------------------------------------|
A|-----------------------------------------------|
E|-----------------------------------------------|

GII

E|---------------------------------|
B|---------------------------------|
G|-5-5-5-5-5---5-5---5-5-5-5-5-5-5-|
D|-5-5-5-5-5---5-5---5-5-5-5-5-5-5-|
A|-3-3-3-3-3---3-3---3-3-3-3-3-3-3-|
E|---------------------------------|

GI

E|-----------------------------------------------|
B|----12-12----12------12---12----12-13-13-12----|
G|-14-------14------14---------14-------------14-|
D|-----------------------------------------------|
A|-----------------------------------------------|
E|-----------------------------------------------|

GII

E|---------------------------------|
B|---------------------------------|
G|---------------------------------|
D|-5-5-5-5-5---5-5---5-5-5-5-5-5-5-|
A|-5-5-5-5-5---5-5---5-5-5-5-5-5-5-|
E|-3-3-3-3-3---3-3---3-3-3-3-3-3-3-|

GI

E|-----------------------------------------------|
B|----12-12-12-12--------------------------------|
G|-14--------------14-14-12-12-12-12-12-12-12-12-|
D|-----------------------------------------------|
A|-----------------------------------------------|
E|-----------------------------------------------|

GII

E|---------------------------------|
B|---------------------------------|
G|-------------------5-5-5-5-5-5-5-|
D|-2-2-2-2-2-2-2-5---5-5-5-5-5-5-5-|
A|-2-2-2-2-2-2-2-5---3-3-3-3-3-3-3-|
E|-0-0-0-0-0-0-0-3-----------------|

Verse (Palm-Muting)

    G
The cool is dead, baby go on and sleep

C
Rest your weary head and lover bury me

G
And in the morning we'll start over again

Em                              C
That's how they do it up on the screen

(Then second guitar plays the riff below palm muted, rhythm no longer palm muted)
    G
See me and my baby we would dance all night
E|-------------------------------------------------|
B|-------------12----------------------14-15-14----|
G|-14-12-14-12----12-14-12-14-12-14-12----------12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

    C
And I would know the steps in my baby's time
E|-------------------------------------------------|
B|-------------12----------------------14-15-14----|
G|-14-12-14-12----12-14-12-14-12-14-12----------12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

   G
To do it like they do for the girls uptown
E|-------------------------------------------------|
B|-------------12----------------------14-15-14----|
G|-14-12-14-12----12-14-12-14-12-14-12----------12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

  Em                               C
I heard they light 'em up like the blues
E|-------------------------------------------------|
B|-------------12----------------------------------|
G|-14-12-14-12----12-14-12-12-12-12-12-12-12-12-12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

Pre-Chorus

So I'm waiting (so I'm waiting)

E|-------------------------------------------------|
B|-------------------------------------------------|
G|-12-12-12-12-12-12-12-12-11-11-11-11-11-11-11-11-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

And she's waiting (and she's waiting)

E|-------------------------------------------------|
B|-------------------------------------------------|
G|-------------------------------------------------|
D|-14-14-14-14-14-14-14-14-12-12-12-12-12-12-12-12-|
A|-------------------------------------------------|
E|-------------------------------------------------|

For us to remember................

E|----------------------------------------------|
B|-------------------------------------12-------|
G|-------------------------------12h14----12-12-|
D|-/12-12-12-12-12-12-12-12-12h14---------------|
A|----------------------------------------------|
E|----------------------------------------------|

Chorus

So was I good to you, the wife of my youth?

E|----------------------------------------|
B|----------------------------------------|
G|-------1212-11-12-12-11-----------------|
D|------------------------14--14-12-12-12-|
A|----------------------------------------|
E|----------------------------------------|

   Not another soul could love you like my rotten bones do, so

E|-------------------------------------------------------------|
B|-------------------------------------------------------------|
G|-------------------------------------------------------------|
D|-12h14p12---12---12----12h14----12---------------------------|
A|-------------------------------------14-14-14-14-14-12-12-10-|
E|-------------------------------------------------------------|


    I would wait on the edges in between

E|--------------------------------------|
B|--------------------------------------|
G|-12-12-11-12----12-11-----------------|
D|-----------------------14-14-14-12-12-|
A|--------------------------------------|
E|--------------------------------------|


   These New      York streets, where you and I would meet

E|------------------------------------------------------|
B|----------------12------------------12----------------|
G|-------12-12h14-----14///////-14-----------14-12---12-|
D|-12h14------------------------------------------------|
A|------------------------------------------------------|
E|------------------------------------------------------|


Then play intro again.


Verse 2 (Palm muting)

    G
For twenty nine years we loved that line

    C
And I would take it easy if I had your mind

    G
But I'm a cannonball to a house on fire

(no chord here)
And you're slow like Motown soul

(Then second guitar plays the riff below palm muted, rhythm no longer palm muted)
    G
So what man wouldn't love her with her long black hair?
E|-------------------------------------------------|
B|-------------12----------------------14-15-14----|
G|-14-12-14-12----12-14-12-14-12-14-12----------12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

   C
If I cut you up maybe I came to bear
E|-------------------------------------------------|
B|-------------12----------------------14-15-14----|
G|-14-12-14-12----12-14-12-14-12-14-12----------12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

   G
To bandage your wounds with the salt on my tongue
E|-------------------------------------------------|
B|-------------12----------------------14-15-14----|
G|-14-12-14-12----12-14-12-14-12-14-12----------12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

  Em                     C
And I'm the only one not here
E|-------------------------------------------------|
B|-------------12----------------------------------|
G|-14-12-14-12----12-14-12-12-12-12-12-12-12-12-12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

Pre-Chorus

So I'm waiting (so I'm waiting)

E|-------------------------------------------------|
B|-------------------------------------------------|
G|-12-12-12-12-12-12-12-12-11-11-11-11-11-11-11-11-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

And she's waiting (and she's waiting)

E|-------------------------------------------------|
B|-------------------------------------------------|
G|-------------------------------------------------|
D|-14-14-14-14-14-14-14-14-12-12-12-12-12-12-12-12-|
A|-------------------------------------------------|
E|-------------------------------------------------|

For us to remember................

E|----------------------------------------------|
B|-------------------------------------12-------|
G|-------------------------------12h14----12-12-|
D|-/12-12-12-12-12-12-12-12-12h14---------------|
A|----------------------------------------------|
E|----------------------------------------------|

Chorus

So was I good to you, the wife of my youth?

E|----------------------------------------|
B|----------------------------------------|
G|-------1212-11-12-12-11-----------------|
D|------------------------14--14-12-12-12-|
A|----------------------------------------|
E|----------------------------------------|

   Not another soul could love you like my rotten bones do, so

E|-------------------------------------------------------------|
B|-------------------------------------------------------------|
G|-------------------------------------------------------------|
D|-12h14p12---12---12----12h14----12---------------------------|
A|-------------------------------------14-14-14-14-14-12-12-10-|
E|-------------------------------------------------------------|


    I would wait on the edges in between

E|--------------------------------------|
B|--------------------------------------|
G|-12-12-11-12----12-11-----------------|
D|-----------------------14-14-14-12-12-|
A|--------------------------------------|
E|--------------------------------------|


   These New      York streets, where you and I would meet

E|------------------------------------------------------|
B|----------------12------------------12----------------|
G|-------12-12h14-----14///////-14-----------14-12---12-|
D|-12h14------------------------------------------------|
A|------------------------------------------------------|
E|------------------------------------------------------|

Bridge

                                          And only

E|-------------------------------------------------|
B|-------------------------------------------------|
G|-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

   I..........................................can

E|-------------------------------------------------|
B|-------------------------------------------------|
G|-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

   Heal...............your wounds.

E|-------------------------------------------------|
B|-------------------------12-12-12-12-12-13-12----|
G|-14-14-14-14-14-14-14-14----------------------14-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

Only I..........................................can

E|-------------------------------------------------|
B|-------------------------------------------------|
G|-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

   Heal...............your wounds.

E|-------------------------------------------------|
B|-------------------------12-12-12-12-12-13-12----|
G|-14-14-14-14-14-14-14-14----------------------14-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

   When you can't       go on
E|-------------------------------------------------|
B|-------------------------------------------------|
G|-12-12-12-12-12-12-12-12-------------------------|
D|-------------------------12-12-12-12-12-12-12-12-|
A|-10-10-10-10-10-10-10-10-------------------------|
E|-------------------------10-10-10-10-10-10-10-10-|

   And can't go on

E|-------------------------------------------------|
B|-------------------------12-12-12-12-12-13-12----|
G|-14-14-14-14-14-14-14-14----------------------14-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

   And you can't       go on
E|-------------------------------------------------|
B|-------------------------------------------------|
G|-12-12-12-12-12-12-12-12-------------------------|
D|-------------------------12-12-12-12-12-12-12-12-|
A|-10-10-10-10-10-10-10-10-------------------------|
E|-------------------------10-10-10-10-10-10-10-10-|

   When you know

E|-------------------------------------------------|
B|-------------------------------------------------|
G|-14-14-14-14-14-14-14-14-14-14-14-14-14-14-14-14-|
D|-------------------------------------------------|
A|-------------------------------------------------|
E|-------------------------------------------------|

  Hold on

E|----------------------------|
B|----------------------------|
G|-7-7-7h9------------7-7-7h9-|
D|----------------------------|
A|----------------------------|
E|----------------------------|


Was I good to you, the wife of my youth, not another soul could love you like

E|----------------------------|
B|----------------------------|
G|-7-7-7h9------------7-7-7h9-|
D|----------------------------|
A|----------------------------|
E|----------------------------|

My.........

E|----------------|
B|----------------|
G|-12-12-12-11-11-|
D|----------------|
A|----------------|
E|----------------|



Chorus

So was I good to you, the wife of my youth?

E|----------------------------------------|
B|----------------------------------------|
G|-------1212-11-12-12-11-----------------|
D|------------------------14--14-12-12-12-|
A|----------------------------------------|
E|----------------------------------------|

   Not another soul could love you like my rotten bones do, so

E|-------------------------------------------------------------|
B|-------------------------------------------------------------|
G|-------------------------------------------------------------|
D|-12h14p12---12---12----12h14----12---------------------------|
A|-------------------------------------14-14-14-14-14-12-12-10-|
E|-------------------------------------------------------------|


    I would wait on the edges in between

E|--------------------------------------|
B|--------------------------------------|
G|-12-12-11-12----12-11-----------------|
D|-----------------------14-14-14-12-12-|
A|--------------------------------------|
E|--------------------------------------|


      And I would wait on the edges in between

E|-------------------------------------------|
B|-------------------------------------------|
G|-------12-12-11-12----12-11----------------|
D|-12h14----------------------14-14-14-12-12-|
A|-------------------------------------------|
E|-------------------------------------------|

     And I would wait on the edges in between

E|-------------------------------------------|
B|-------------------------------------------|
G|-------12-12-11-12----12-11----------------|
D|-12h14----------------------14-14-14-12-12-|
A|-------------------------------------------|
E|-------------------------------------------|



These New      York streets, on These New  York     streets
E|--------------------------------------------------------|
B|----------------12-----------------------------12-------|
G|-------12-12h14-----14///////-12----12///12h14----14///-|
D|-12h14--------------------------------------------------|
A|--------------------------------------------------------|
E|--------------------------------------------------------|


  Where you and I would meet

E|------------------------|
B|------12----------------|
G|-14----------14-12---12-|
D|------------------------|
A|------------------------|
E|------------------------|

Thanks.