Two small Bavarian villages argued in a friendly way that they each had the best concertina player. So they decided to hold a contest to see which musician was the best. The winner would get a prize pig. There was a lazy young boy, Droopsi, who only wanted to play a concertina, even though he was awful! When his village's musician is hurt and can't play, they must depend on Droopsi to win the pig. A cute story with an unexpected ending.
A good one in the tradition of Kahl's masterpiece The Duchess Bakes a Cake. This one is not done in rhyme, but there are plenty of wonderful repetitions that hold it together.
Tip: read this one with an overdone German accent (walrus mustache optional). It's just begging for it. Also let the rhythmic word pairings in those long lines accelerate like a runaway wagon barreling down a steep hill.
When he pulled the concertina, it would squeak. When he pushed the concertina, it would squawk. When he squeezed, it wheezed. And Mamma and Papa and Trudl and Rudl and Hansl and Franzl and Fritzi and Mitzi would cover their ears with their hands and tell him to please go up to the mountains to practice. "You'll never learn to play, Droopsi," Papa would say. "You'd better learn to make cheeses."