M'self, I like Michael Cooney's version, which I think derives from Hudie Ledbetter's, and includes verses like:

Weepin' willow, and the mournin' dove
Corinna, Corinna, you the one I love

Sometimes I think, babe, you're too sweet to die.
Other times I feel, you oughta be burned alive.

I'll chop your wood babe, I'll even tan yo' hide
I'll make you happier than any man alive

Goin' down to the river, gonna set down on a log
If I can't be the one you love, I sho' won't be your dog.

Is this the same song y'all are talking about? I think it's called "Corinna" or "Sweet Corrina".
Blessings,
Barbara