This thread is superb! My dad sang this to my sister and I, as it was sung to him by my grandmother. Our version has one slight variation:

Go to sleep
My little pickaninny
Br'er fox is gonna getcha if ya don't
Slumber on the bosom of your ole' Mammy Jenny
Mammy's gonna smack ya if ya don't
L'loo, l'loo
Underneath the silvery, southern, moon
Rockabye, hushabye,
Mammy's little baby
Mammy's little Alabama coon

He also sang us this one:

Oh, the little dog barked at the big round moon
As it rose in the eastern sky
He said, "I'm a terror, although I am small
And I dare you, you impudent fellow to fall,"
But the moon only smilled and smiled
The moon only smiled and smiled