Roy's typical song will be Adele's Set Fire to the Rain. When he's in a particularly good mood or sassing others it might start to resemble this popular Disney tune with some lyrics rewritten and different instruments. Aaaand here's an extra tune from canon for kicks.

When he's in close proximity to Riza Hawkeye, their songs tend to harmonize and turn into something of a mash up of their themes. His individual song also tends to sound more clear and correct in her presence.

Until he's rescued his main song will likely be warped in a way that makes it sound less serious and soulful than it is meant to be.

Edit And a last minute suggestion I liked. The Phoenix by Fall Out Boy.