There's a version recorded on a lovely CD: Various Artists 'Georgia Folk: A Sampler of Traditional Sounds' Global Village Music CD 03. It is performed by Ray Favors - with body patting, mouth popping etc - and was recorded by Dave Evans in 1970.

HAMBONE

Hambone, hambone have you heard
Papa gonna buy me a mockingbird
If that mockingbird don't sing
Papa gonna buy me a diamond ring
If that diamond ring don't shine
Papa gonna buy me a nanny goat
It that nanny goat don't rate
Papa gonna whup my boom-de-yay
Hambone!

Hambone, hambone where you aye (?)
In the chicken house cookin' rye
Hambone, hambone where you bin
Round the world and I'm goin' agin
Hambone!