Ballad of St. Ann's Reel and the tune to go with it for sure.

Unicorn Song (Irish Drunks seem to love this song by a Jewish songwriter)
Water is Wide/Carrickfergus
Most of the O'Carolan tunes.

Most of the Niel Gow tunes
Danny Boy
Loch Lomond
J Scott Skinner Tunes
Some of the Jerry Holland tunes
Murshin Durkin
Long Black Veil
Black Velvet Band
Most of the Makem/Clancy Reperitoire (After all they invented the genre, didn't they?)
Evans and Doherty songs
Any number of sea songs and chanties/shanties.

There's a bit of a start. I'm sure you'll have a ton (well just what you've gotten so far is a lot).