How incredibly cool. This lullaby was such a private, personal thing and now... it's like finding long lost family ;-)

The version my grandma sang to me in the mid-sixties went like this:

Go to sleep my little pickaninny
The brown fox will get you if you don't
Hush-a-bye, rock-a-bye
Mama's little baby
Mama's little Alabama coon.

I loved it so much (the tune is incredibly soft and sweet) I wanted to share it with my daughters. So I'd morphed it into this:

Go to sleep, my itty bitty baby
The brown fox will get you if you don't
(echo'ed quitely: if you don't)
Hush-a-bye, rock-a-bye
Dady's little baby
Dady's little itty bitty boo.

Thanks so much to all for posting the info here.