It seems the idea of a composer has become so vague for many English speakers that the word itself is being co-opted as a sort of discount substitute for composure. (The proper term for this is an eggcorn, coined by the fine minds over at Language Log.) Google turns up the following:
(All the other permutations I tried had at least a handful of examples.)
A number of these come from lyrics to hip-hop songs, but I’m nowhere near cool enough to know whether it’s an actual variant in the urban lexicon or just bad transcription. “Maintain my composer” (30 hits) appeared in an unusual number of NC-17 sources, which I suppose could be considered either flattering of frightening. As far as I could tell, only this was consciously making a pun.
On the plus side, our friend Mark Meyer noted in a comment that his computer’s spellchecker keeps insisting that “Poulenc” should be “opulence.” So there’s hope.