This is part of the first page of a search in Altavista for "Irish songs MIDI" :

1. Welcome To "TRAD" - Traditional Irish Music TRAD - Traditional Irish Music... URL: www.firepowr.com/ Last modified on: 30-Jan-2000 - 4K bytes - in English 4. The Island-Midis and Links Midi music and surfin' links to midi music files, celtic, folk, classical and religious music, chemistry, multiple sclerosis and web page resources. URL: www.bardstown.com/~ttipton/index.html Last modified on: 11-Jul-1999 - 25K bytes - in English [ Translate ] [ More pages from this site ] [ Company factsheet ] 6. Ultimate MIDI Page Huge MIDI Music Directory, with tons of files, links, software, & more... URL: www.ultimatemidi.com/ Last modified on: 2-Feb-2000 - 20K bytes - in English [ Translate ] [ More pages from this site ] [Related pages ]

FirePowr has a good collection in ABC format (you may download ABCMus11.exe from their link), The Islands has many midis, and there are good links to other places. Sorry for not suggesting something more original, but I'm no specialist, I hope this helps.
Yours, Andrés