My mum sang a similar version,(with Southern words and an English accent) in 2:4 time.
It went something like:

Go to sleep, my curly-headed baby (Bah-bee)
Father Fox will catch you if you don't.
Hush-a-bye, rock-a-bye, my little cherry pie,
Mama's little Alabama coon.

The memories of lovingly-sung lullabies bring comfort and I whisper them to my children now, as did the generations before me.