Being deaf I may have the words wrong but this is the version I seen to have in my memory from about the 1950's on:

Go to sleep my little picanninie
Mama's going to smack you if you don't
Right on the bottom of your old panannine (this would mean a nappy or baby pants)
Mr Fox will get you if I don't
Lu la lu la lu la lu la lulu
Right down on the other side of the moon
Hush a bye, don't you cry, Mama's little baby
Mama's little piccanninie coon.