Have you done a 'google' search for "Armenian song midi files" ?
I have NO idea what the songs are but here are a couple of sites...
http://www.geocities.com/armenian_midi/

this site even has some 'scores' for the songs:
http://mousaler.com/songbook/data/patriotic.html

scroll down the page on this one:
http://jdemirdjian.com/Armenians.htm


Good luck
t.