There are no rhymes in Woody Guthrie's Plane Wreck at Los Gatos - unless you count Rosalita and Maria. But I bet most people hearing it or singing it don't even notice that. (It's not in the DT, for odd copyright hassle reasons, but you can check at that link I gave there.)

Metre and especially stress is far more important than rhyme in English verse. And especially when it comes to singable verse.