No doubt many of the Irish people on the list are sick of this quotation from Chesterton, but how can I pass it up with a set-up like this?

The Great Gaels of Ireland
Are the men that God made mad,
For all their wars are merry,
And all their songs are sad.

(GKC was no more than half right.)

Anyway, for Irish songs in which your lover doesn't leave, your dog doesn't die, your pickup doesn't break down (oh, sorry, wrong genre), you might try Thomas Moore's Irish Melodies, for instance, "Believe Me, if All Those Endearing Young Charms". I just searched for "Irish Melodies" and found only two songs from this collection in the DT! But also in the DT is the overlong but charming "Rory O'More".

A search of the DT for "@ribald" might turn up some good possibilities, if you like to sing such songs.