Heard this at the end of HIMYM and was devastated to find out it wasn't here, 
worked it out fairly quickly and this is what I came out with, sounds pretty decent to me.

I didn't work out the lead but if you want to make up some stuff its mainly on the B string.

There's a capo on the 3rd fret and all chords are relative to the capo.

 C     : x32010
 C/B   : x22010
 C/A   : x02010
 G     : 320033
 Am7   : xx2010
 Am7/D : xx0010

The picking is pretty basic, its root note then the last three strings.

Main Progression:

   C        C/B        C/A                C                  G
e|-----000------000--|-----000-----000--|-----000-----000--|-----333-----333|
B|-----111------111--|-----111-----111--|-----111-----111--|-----333-----333|
G|-----000------000--|-----000-----000--|-----000-----000--|-----000-----000|
D|-------------------|------------------|------------------|----------------|
A|--3--------2-------|--0-------0-------|--3-------3-------|----------------|
E|-------------------|------------------|------------------|--3-------3-----|

Alternative Progression:

   C        Am7        Am7/D     C         C       C/B      C/A
e|-----000------000--|-----000-----000--|-----000-----000--|-----333-----333|
B|-----111------111--|-----111-----111--|-----111-----111--|-----333-----333|
G|-----000------000--|-----000-----000--|-----000-----000--|-----000-----000|
D|-----------2-------|--0---------------|------------------|----------------|
A|--3----------------|----------3-------|--3-------2-------|--0-------0-----|
E|-------------------|------------------|------------------|----------------|

Intro:

| C  C/B | C/A     | C     | G      |

C               C/B              
Sometimes I wake up with a sadness,
C/A
Other days, it feels like madness,
C                G
So, what would I do without you.

C               C/B       
When colours turn to shades of grey,
C/A
With the weight of the world at the end of the day,
C                G
Oh, what would I do without you.

C            Am7         Am7/D       C
A decade goes by without a warning,
C                  C/B               C/A
And there's still a kindness in your eyes,
C           Am7             Am7/D    C
Amidst the questions and the worry,
C                     C/A
A peace of mind always takes me by surprise.


Interlude:
| C  C/B | C/A     | C     | G      |


C                           C/B
I feel like I'm walking with eyes as blind,
C/A
As a man without a lantern in a coal mine,
C                G
Oh, what would I do without you.

C                      C/B
My imagination gets the best of me,
C/A
And I'm trying to hide lost at sea,
C                G
Oh, what would I do without you.

C                     Am7               Am7/D       C
The difference between what I've said and done,
C               C/B             C/A
And you're still standing by my side,
C       Am7        Am7/D     C
A guilty soul and a worried mind,
C                    C/A
I will never make it if I'm on my own.

C                     C/B
So you got the morning I got midnight,
C/A
You are patient I'm always on time,
C                G
Oh, what would I do without you.

C                    C/B
You got your sunshine I got rain clouds,
C/A
You got hope I got my doubts,
C
So, what would I do without you,
C                C/A
Oh, what would I do without you,
C        (Pause)
Oh, what would I do without you.

Outro:

Repeat

| C  C/B | C/A     | C     | G      |