I was looking at some of the prophets and occasionally they have songs in them, I'm not sure if this has been discussed or not, or whether or not that is enough to have them musicians, but either way, here's what I found:
Ezekiel: 19, 27, 32:1-2
Amos: 5:1-2
Habakkuk 3
These seem to be songs (I'm not always sure where things end, but they usually begin with something like "Sing this song to..." and Habakkuk ends with "To the choirmaster: with stringed instruments."