I did some looking, and it's not as easy as you'd think to locate the songs. Yes, there are sites with Irish songs, but they give you a long list of titles without letting you know which are 6/8. Sometimes they say they have songs, but they are actually dance tunes with no lyrics.

Go to your public library and see if they have the Celtic Fakebook by Hal Leonard. I own this book, and there are 7 or so 6/8 Irish songs with lyrics just in the A's and B's. The chords are there, too.

If you find the book, all you have to do is copy the songs you like.