Jamaica Farewell is fun and not difficult. Also, sea shanties like Bold Riley and Blow the Man Down.
Most "Fun" Pieces.
Anne, people will certainly post lists of their favorite tunes, and there is indeed a value in that. But I would like to point out that the three songs you mentioned are all traditional fiddle tunes. Maybe you just like fiddle tunes (and guess, what: I do, too)! If that is the case, you are in luck because there are thousands of them out there.
You might peruse some of the online catalogues of fiddle tunes such as the Fiddle Tune Archive of the Old Towne School of Folk Music or Hetzler's Fakebook . I will sometimes look through lists of fiddle tunes and examine either those that I've heard mentioned in dulcimer conversations or just those with a funny name and give 'em a listen. If one sounds like it's not too hard and its fun, I'll try to learn it. Hetzler's Fakebook separates tunes in different keys, so you can just concentrate on tunes that are traditionally played in D.
When I find a fiddle tune I want to learn I start out just googling its name followed by "dulcimer tab." Sometimes you get lucky and find the tab. And if not, you might be able to learn it by ear. But you can always find standard music notation and work that route if you can. The next step is to find renditions of it on YouTube and listen long enough to get the basic melody in your head. It's a lot easier to play a song on the dulcimer that you have already memorized in your head.
By the way, one tune that is common in dulcimer circles now but is perhaps not as well known is Elk River Blues. It is not really a blues but a "crooked" fiddle tune by Ernie Carpenter. If you search the videos and music here you will find a half-dozen versions or so, some noter drone and some with chords (like mine). The song sounds more complicated than it is and just has this easy-going roll to it, like the flow of a river. To me it is much easier to play than Turkey in the Straw, though I like that tune, too.
Dusty T., Northern California
As a musician, you have to keep one foot back in the past and one foot forward into the future.
-- Dizzy Gillespie
updated by @dusty-turtle: 07/25/16 03:12:08AM
Can't post them if they're copyrighted...
I like Spotted Pony, Columbus Stockade Blues, Rock the Cradle, Joe, Rosin the Beau, Old Yellow Dog...I'm sure there is tab for some of these on Everything Dulcimer (which has a HUGE archive of tab for public domain tunes.)
Jan Potts, Lexington, KY
"Use what talents you possess; the woods would be very silent if no birds sang there except those that sang best." Henry Van Dyke
Pieces like 'Turkey in the Straw', 'Hangman's Reel' and 'John Stinson's no.2', are such fun to play, and not too hard, (at a basic level). I was wondering what else, in this vein, people particularly like. They don't get a lot of exposure 'down' here in Oz ...