The Hollies’ song “Carrie Anne” doesn’t rhyme very much. There a couple of near rhymes (“I played a janitor, you played a monitor”, and “never caring/disappearing”), but most of the song doesn’t rhyme.
There’s an old song called “Moonlight in Vermont,” which has been recorded by such folks as Ella Fitzgerald, Frank Sinatra, and Sam Cooke, among others, whose lyrics don’t rhyme.
