If one MUST bowdlerize this great old song, seems to me that the best substitute for "darkies" is "home-folks". "The people" is just took generic, and somehow, although in two syllables, just doesn't have the right cadence.

And as to "gay", it has its old meaning still, and I (for one) refuse to abandon it just because it has been widely misapplied in the modern day. The context makes clear, I think, that it's not that modern usage.

In context, "the home-folks are gay" fits the mood of the song, although not the detailed original meaning.

Dave Oesterreich