How can I transfer old music to my new iPhone?

When I was a kid, I bought music under my parents' apple id. I've authorized my computer for both my parents' apple id, and my own, but when I sync the library to my phone, all the old songs say, "This item is not currently available in your country or region". Am I missing a step? Is there a way to authorize my phone? My computer plays all of the songs just fine.

[Re-Titled By Moderator]