Another Thomas Moore song that isn't too melancholy and has a pretty tune is "The Pretty Maid Milking The Cow".

http://ingeb.org/songs/itwasona.html
(Cailín Deas Crúite Na Mbó, or colleen dhas cruthen na moe ) Pretty Maid Milking the Cow (or It Was On A Fine Summer Morning).

One of my favorite standards for both tune and lyrics that aren't sad is the old love song (not the rebel version) of the Foggy Dew.

alice in montana