Landlords are supposed to register with the Private residential Tenancies Board - but a lot of them don't even though it's supposed to be an offence not to.
Anyway - if he/she has - then there is a public register for each county available. It's not very well organised and it's in MS Excel format. Some of the entries show the landlords name (most don't!) But maybe the PRTB will let you know who it is if they have registered? The register is here ... http://www.prtb.ie/pubreg.htm
another way to do it, which some one else may have more knowledge about is to get the OS map of the plot the house is on, then send that to the land registry who will give you the folio number and the name(s) of who the land is registered to. there is a small fee for this which i think is about six yoyos.
have fun