I've been doing this song for years and I believe the correct chords are as follows.These were taken from an old song book of Mac Wiseman
G             C                        G
Well I wonder how the old folks are at home
G                                  C
I wonder if they miss me when I'm gone
C
I wonder if they pray
G                     E
for the boy who went away
A                                 D
and left his dear old parent all alone