My Mum and Gran used to sing this to us when we were little. We thought that they had made it up. They were from London, my gran was born in White Chapel in 1880 ad my Mum in Camden in 1922, .
They used to sing these words

Go to sleep my little picaninny
Bear 'n' fox'll catch ya if ya don't
Slumber on the bosom of your old mamma Ginny
Bear and fox'll catch ya if ya don't!
Noo nah, noo nah, noona noona naddy ,
Underneath the silvery, silver moon
Hush-a-bye
Don't you cry,
Mammy's little babby,
mammy's little ala bala boo.