Hi,There are usually quite a few hymns set to the tune "O Waly Waly" (better known as "The Water is wide".
Another nice one is to do "I heard the voice of Jesus say" to the tune of "Mary from Dungloe".
Then of course there's "There is a green hill far away", to "the house of the rising sun." There's quite a few to "Londerry air" or "Danny boy" too.
Some beautiful old Irish tunes are "Moville", "Durrow", and "Clonmacnoise"(used for the 2nd part of St Patrick's breastplate..... "Christ be in me, Christ within me....etc." Have a go looking in the index of tunes, like Joe already suggested.
I used to play church organ and was always trying to find good tunes, so please let us know if you find any.
Slainte
Alison