Update: I've done a good bit of work on this since I initially wrote this blog post and now I have since settled on the F-major version.
Last weekend at the Northern VA Ukulele Meetup, someone brought a copy of "I only want to be with you" by Dusty Springfield. And the first two chords are C and A minor. And I thought I heard a familiar song and this one shook out of the tree, so to speak.
Hallelujah, which I think is originally written by Leonard Cohen. But, just about everyone has a cover version because it is a gorgeous tune with emotional complexity. It's like a good cup of coffee actually. And I don't mean the sugar-laden version that most people drink.
I also added a transposition to they key of F.