I'm forcing my dad to help me with this search, but I can offer more than he can. I was able to catch some of the lyrics, though not all, and probably not correctly. This is what I might have, though.

Oh, the cuckoo She's a pretty bird And she warbles When she flies

She don't ever ************* ************* Out to fly

Old Johnny He done got me (or don't, or doesn't) And he has me Here to die

Well that sentry He ain't no fear Like a cuckoo I will fly

Gonna build me An ol' cabin On a mountain Far away

Gonna live there With my true love Till we both do Pass away

The song is very simple, with a range of maybe five notes, and sounds minor. I don't know if all that I have here is correct. For anyone who wants to check out the movie, it's Andersonville, made for TV in 1996, and first aired on TNT. The movie is very well done, was nominated for three awards, received one of them, and is--to the best of my knowledge--historically accurate. Please tell me anything that might be of assistance.