One problem might be that those are pretty common song words in any language. I don't know, I'm not really into Japanese music, but even I know songs like 一人 by Ayumi and 上を向いて歩こう by 坂本九.
I went to YouTube and searched the terms 一人 心 and tons of results came up. Maybe one of them are it, and if not maybe you'll find something else you like.