This is an interesting question! Well, I often find that that one song on an album that didn't click with me at first, that I thought sounded bad and skipped, becomes my favorite song period for a while after giving it a second (often more) chance, so I'm sure that some music I find to be bleh could grow on me.
Chances are though, especially if it's hip-pop-dance-autotune-love song-hop I'd get more and more annoyed the more I heard it, so I may just go with nothing. I usually like to sing when I'm all alone anyways, so that may be my alternative. Plus, the ocean sounds nice, and when you say desert island, I'm assuming you mean a moderately large sized island with trees and stuff as opposed to the tiny island with one tree on it like in cartoons, so like BassDriver, I'd probably make my own instruments.