Some that won't offend modern parents or kindergarten teachers, so that you can sing them with little kids:

Dance him east and dance him west (3x)
Then you both will want to rest

Hand her to her mommy-o (3x)
That'll make her calm-y-o

Drive him round and round the block (3x)
If you can't make the cradle rock

Let her have her blankie-o (3x)
Then she won't be cranky- o

And instead of pouring "a little moonshine" in his mouth,substitute "warm milk."