Rogers and Clarke
Warren Beatty was Lyle Rogers and Dustin Hoffman was Chuck Clarke, the singing songwriting duo in the deservedly underrated 1987 flop Ishtar. The first 20 minutes or so when they team up and start writing songs actually isn't that bad, but then the plot clumsily lurches into gear and everything goes straight to hell. Their awful songs are pretty funny. I enjoy "Telling the Truth is a Dangerous Business" for some reason.
Diminutive '70s singer songwriter Paul Williams apparently penned many of the deliberately bad songs. And dammit, there's no soundtrack album for this movie!