I searched on the internet for Irish hymns--seems they are few and far between.
I did find a few Celtic and Celtic inspired hymns, though:
Sometimes a Light Surprises
Come Thou Fount of Every Blessing
Morning Has Broken
Simple Gifts
Be Thou My Vision
May the Road Rise Up to Meet You
Abide With Me
Wexford Carol (technically a Christmas carol, but one of the only Irish religious songs I could find)