Okay, this is really funny... I'm the youngest of four--all raised as JWs. My mom sang a certain lullaby to all four of us; it was by far the one she sang the most. We always called it "Skeeters Am A-Hummin'," but I just Googled it and found out it was originally called "Kentucky Babe." Here are the lyrics as I remember them--and, remember, my family is lily white.
Skeeters am a'hummin round that honeysuckle viiiine. Sleep Kentucky Baaaabe.
Sandman is a'comin' for that little babe of miiine. Sleep Kentucky Baaabe.
Silvery moon's a'shining in the heavens up above. Bobolink's a'pinin' for his little lady loooove.
You're sure mighty lucky. Babe of old Kentucky. Clooooose yoooour eyyyyes and sleeeep.
Flyyy awayyyy. Fly away Kentucky babe. Fly away to rest.
Flyyy awayyy. Lay your kinky, wooly head upon your mammy's breast. Clooose yooour eyyyyes and sleeeeeeeeep.
I'm telling you, I was nearly THIRTY before I realized the humor in our mom singing this song to us. "Lay your kinky, wooly head upon your mammy's breast"?! Just never thought about it. Turns out she was singing a "plantation lullaby," according to some of the sources I'm finding online. The full lyrics, which either Mom didn't sing--or I just can't remember, include things such as "possom fo' your breakfast," addresses the child being sung to as "little colored lady," and actually uses "little coon" instead of "little babe."
Mom grew up in the 30s and 40s in a small Tennessee town. She always spoke of how her entire family, including all the cousins, aunts, uncles, etc. would get together in big barns and sing and harmonize. I guess they added plantation lullabies to their repertoire.