I agree with Mike. It is a very expensive business trying to research your Irish Roots. I have been dipping in and out of mine for nearly 20 years now, with very little found. There is more coming online now, but when I started I paid for baptism information from one of the Heritage Centres that they have in Ireland.
My 2 x gt.grandparents are from Donegal and Dublin. It was my Donegal ancestor that I had some information for from the Heritage Centre. I visited Ireland and made prior arrangements with the Cannon of the Church in St Johnstown to look at the church, and look at the registers which he held. I didn't find out any more than I knew but it was brilliant to be able to look at these old books and the places where my ancestor lived. Basically it was part of an old farm in the middle of nowhere!!
My other 2 x gt.grandparents are also from Ireland (and they also lived in London Prentice Street). I know that one was from Roscommon as it was on the census - but where!!? My 2 x gt.grandfather, Michael Gilmartin, just gave Ireland on the census. But I think it may have been Roscommon or Sligo as that is where there is most concentration of the surname Gilmartin/Kilmartin.
Most of the Irish records were burned in the fire at the Four Courts in 1922, so it is pretty difficult to find anything. Perhaps a trip to PRONI at Belfast is my next project. However for you at the other end of Ireland perhaps you should contact the Limerick Heritage Centre for a quote (not cheap) and to see what they hold.
The Limerick Archives, The Granary, Michael Street, Limerick.
This site has good information and addresses:
https://www.kinsella.org/genealogy/research/intsearc.htm
Good luck.
Judy