There are loads of Irish songs in the public domain. Just check each one out if you're not sure, as the Irish are quick to claim songs from all over the place and say they're Irish and traditional, when in fact they're neither. Dirty Old Town is a good example, being a song about a town in Lancashire composed by a Scottish/English singer. Another one that isn't Irish or trad is "Green Fields of France", which isn't even its real title but you know the one I mean.

The list you've found has lots of good stuff in it from Britain and Ireland. Whether a song is actually Irish or not matters less, as there are no legal complications. I'm sure you can find plenty there without infringing copyright.