I think this is how the song is played. Not 100% sure, but it should do.

Standard tuning.
Capo 1.

Chords played:
Em    -0-2-2-0-0-0- or Em7   -0-2-2-0-0-3-
D     -x-x-0-2-3-2-
C     -x-3-2-0-1-0- or Cadd9 -x-3-2-0-3-3-
Dsus2 -x-x-0-2-3-0-
G     -3-2-0-0-3-3-


Verse 1:


            Em       D C
And she was just
             Em      D C
another lullaby
                 Em       D C
with candlelight eyes
               Em         D C
singing you to sleep,
            Em        D C
drowsy with heat.


             Em       D C
And you were just
             Em       D C
a warning to avoid
                Em       D C
asleep upon the soil,
             Em           D C
holding onto night,
                 Em          D C
fading with its' light.
                 Em         D C
Fading with its' light.


Chorus:


Cadd9                      G                      Em7
      And your heart was a bird, scared still and alone
                   D
and the only thing she ever cared for
Cadd9                         G
      with wings tattered and torn,
                 Em7                   D  Dsus2
beating unevenly,   beating unevenly.
Cadd9                      G                      Em7
      And your heart was a bird, scared still and alone,
             D
and the only thing she ever cared for.
Cadd9                    G
      And your heart was forgotten, 
             Em7
alone on the floor.
              D                 Em         D C
She picked it up, brushed it of dust.
              Em          D C
Brushed it of dust.


Verse 2:


             Em        D C
And you were just
                 Em           D C
a love-drunk vagabond
                           Em         D C
with little reason to hold on.
                    Em           D C
Pressed against the glass,
                Em            D C
watching people pass.
                Em            D [C]
Watching people pass...


Chorus:


Cadd9                      G                      Em7
      And your heart was a bird, scared still and alone
                   D
and the only thing she ever cared for
Cadd9                         G
      with wings tattered and torn,
                 Em7                   D  Dsus2
beating unevenly,   beating unevenly.
Cadd9                      G                      Em7
      And your heart was a bird, scared still and alone,
             D
and the only thing she ever cared for.
Cadd9                    G
      And your heart was forgotten, 
             Em7
alone on the floor.
              D                 Em         D C
She picked it up, brushed it of dust.
              Em          D C
Brushed it of dust.


Verse 3:


Em          D  C
    And you both intermingled
Em        D C
    beautiful, and as simple...
Em          D  C
    And you both intermingled...
Em          D     C         Em          D C
    beautiful and simple as dust.
   Em        D C
As dust.


Chorus:


Cadd9                      G                      Em7
      And your heart was a bird, scared still and alone
                   D
and the only thing she ever cared for
Cadd9                         G
      with wings tattered and torn,
                 Em7                   D  Dsus2
beating unevenly,   beating unevenly.
Cadd9                      G                      Em7
      And your heart was a bird, scared still and alone,
             D
and the only thing she ever cared for.
Cadd9                    G
      And your heart was forgotten, 
             Em7
alone on the floor.
              D                 Em         D C
She picked it up, brushed it of dust.
              Em          D C
Brushed it of dust.


Verse 4:


             Em         D C
And you were just
        Em            D C
another lullaby
                 Em          D C
with candlelight eyes
               Em            D C
singing her to sleep,
               Em          D C~
singing her to sleep.