I play this song in normal tuning using F# Bb and C, it works.

F#                        Bb
I am a man of constant sorrow
             C              F#
I've seen trouble all my days
F#                       Bb
I bid farewell to old Kentucky
                C                      F#
The place where I was born'd and raised
F#                C                    F#
(The place where he was born'd and raised)

F#                                Bb
For six long years I've been in trouble
            C                    F#
No pleasure here on earth I found
F#                               Bb
For in this world I'm bound to ramble
              C                  F#
I have no friends to help me down

F#               C                 F#
(He has no friends to help him down)

F#                                 Bb
It's fare thee well my old true lover
            C                  F#
I never expect to see you again
F#                                  Bb
For I'm bound to ride that northern railroad
             C                  F#
Perhaps I'll die upon this train
F#              C                 F#
(Perhaps he'll die upon this train)

You can bury me in sunny valley
For many years where I may lay      This verse not on "O' Brother" version
And you may learn to love another
While I am sleepin' in my grave
(While he is sleepin' in his grave)

F#                                   Bb
Maybe your friends think I'm just a stranger
              C                   F#
My face you never will see no more
F#                   Bb
But there is one promise that is given
                 C                 F#
I'll meet you on God's golden shore
F#                C                  F#
(He'll meet you on God's golden shore)


The F# is the open F sharp, C is open C, Bb is Barred B moved down one fret