The opne you gave is the only one I know for the verse-- I use these choruses:

Rock the cradle Lucy, rock the cradle high
Rock the cradle Lucy, don't let the baby cry
Rock the cradle Luck, rock the cradle low
Rock the cradle, Lucy, and rock the cradle Joe

and there is the wonderful one I learned from Martha Burns, who denied making it up
I'll go down to MacDonalds, I'll stand there in the line
I'll buy a billion hamburgers and make them change the sign