An all-time favorite, Bobby Darin's wishful classic goes beautifully on the dulcimer, with Larry's piano and Peter's bass creating a great foundation. The only percussion is me striking the dulcimer strings with the side of my hand during that inspired chorus.
I used to retune to get into a major (mixolydian) or minor (ionian) mode, but I have figured out how to work in just one tuning, mixolydian. It's usually D-A-D, but I use C-G-C for a richer sound. My Folkroots dulcimer is off-the-shelf, but it's an inch deeper than most, so its natural resonance combined with a lower tuning gives it a more rounded sound than most dulcimers. I've also been playing it gently for a couple of decades, so the wood cells have aged beautifully. It's a very happy instrument and makes me very happy as I keep finding new ways to get music out of a hunk of wood with just four strings -- and two are doubled, so it's really a three-string instrument.