The Tongue Twister Song from Joe D. Thompson's CD "Every Kind of Magic" has verses based on Peter Piper and Betty Botter, and a chorus something like this:

Oh, my tongue is tied in knots, it's twisted round and round.
Who would have thought that I could get caught and tricked by just a sound?

        I couldn't find a demo of this song (CDBaby had a streaming demo of the CD but it didn't work for me) but you can listen to his Pirates in the Bath for a good laugh. (MP3 demo here 4/5 of the way down the page)
        I enjoy Thompson's music as much as my kid does. My favourite song of his is Stuff (again, demos linked from his site don't work for me) which I heard at a performance last year: "then go to the store/to buy more/stuff to put stuff in." I'm waiting for my copy of his new CD to hear it again.