The one I know is:

Peter, Peter, pumpkin eater
Had a wife and couldn't keep her
He put her in a pumpkin shell
And there he kept her very well.

Peter, Peter, pumpkin eater,
Had another, and didn't love her
Peter learned to read and spell
And then he loved her very well.

I looked in the Oxford Dictionary of Nursery Rhymes and didn't find any others like this. Too bad you can't search the book like you can the Digital Tradition.
-Joe Offer-