Whether or not one thinks the term "morality" necessarily applies to all music (I don't), I would hope that we could all agree that music is a communication medium for meaningful messages. As such, our choices in this realm demand biblically guided thinking and application. The difficulty is often discerning precisely what those messages are.
I've been encouraged in recent years by some who are working to rebuild the discussion of music and meaning out of the ruins of many horrendously bad arguments. In this interview conducted at the recent New Attitude conference, Mohler discusses how we need to be thinking about how not only the words, but also the tune, rhythm, and underlying worldview carry a great deal of meaning. He certainly doesn't provide all the answers, but it seems to me like a pretty useful place to start. In particular, it's accessible to younger people who aren't equipped to handle deep, technical cultural arguments.