The easiest song to play on the mandolin I can think of that doesn't rely too heavily on open strings is "Michael Row the Boat Ashore". Since it's in C Major, you only use four chords, and it never goes above third position. The trickiest part about playing a chord melody to me is getting the chord changes timed right, but this song has a simple rhythm and only four chords to remember. If you want something less challenging than that, I'd say "Somewhere Over The Rainbow." It's in F, so it only uses three open strings, and it goes between two positions for much of the song. Chord melody-wise, just playing around with the melody note can be challenging sometimes. To simplify that, try to think of the song only as an A chord (much like "Michael Row The Boat Ashore" is basically a C chord), bu do what you would if you were playing it over its actual chords. Another simple song I can think of is "Greensleeves." It goes around one position, and it's in an easy key (D major). One more would be the traditional folk song "Golden Slippers," which uses mostly open strings and jumps between two positions. It's very similar to "Mississippi Sawyer," which you might already know if you play clawhammer banjo.