I think the tuning for the version of Down By The River Db Ab Db Gb Bb Db - Half a step 
then double drop d flat. I played along and the sound and the key seemed the same to me.

Tuning - Db Ab Db Gb Bb Db

A - 022010
Bm - 224432 or x24432 or x2443x
C - X32010
Cmaj7 - 032000
D - 000320 or x00320 or xx0320
Em7 - 022010
G - 020030


Em7  A  Em7  A

Em7                 A               Em7
Be on my side, I'll be on your side,

                        A           Em7
there is no reason for you to hide.

                   A                       Em7
It's so hard for me stayin' here all alone

                           A         Cmaj7 or C
when you could be takin' me for a ride,

Cmaj7 or C       Bm                C
She could drag me over the rainbow

               Bm  D  G
and send me away.

     D         A  G
Down by the river,

   D        A  G
I shot my baby.

     D         A
Down by the river,

Em7  A  Em7  A
Daaaaaaaaaaaaaaaaaaaaay (Not sure what he says here, refer to the song)

You take my hand, I'll take your hand,
together we may get away.
This much madness is too much sorrow,
it's impossible to make it today.

She could drag me over the rainbow
and send me away.
Down by the river,
I shot my baby.
Down by the river.

Em7  A  Em7  A

Be on my side, I'll be on your side,
there is no reason for you to hide.
It's so hard for me stayin' here all alone,
when you could be takin' me for a ride.


This might not be perfect, but I think it's pretty close as far as the chords go. listen 
the song and compare, slight alteration may or may not be needed. Hope people enjoy, 
thanks Neil.