Tunjilees.... I can completely understand your frustration and that generally of searching their Irish ancestors.
I'm newish to this too and I only had a couple of names initially, of my g.g. granny living in Dumfries, Scotland:
Julia Lawler / Lollar b. abt 1844 'Ireland'
on her marriage certificate I found her parents were: Catherine Bonn/Burns/Byrne (always take into account how a heavy Irish accent can be transcripted...) Michael Lawler/Lollar (agricultural labourer/ deceased by 1874)
Anyway that was all I had until I was kindly advised (on here) to search the areas close by where Julia was living for other members of her family. I managed to find her mother Catherine and a sister also called Catherine in 1881 and it gave their approximate birth dates and birth places of Carlow and Kildare respectively I've guessed they are protestant (family thing) but my mind is open to other possibilities.
Basically I have found a few more snippets from IGI but havent really got further (lawler seems a bit common).
So what I'm advising is patience and you will start chipping away slowly. But don't expect the fast online finds you get with Scots records.
I also know Lees family in Magherafelt area but unless Tunjilees has since the last postings discovered where in Ireland the family did come from there's little point in finding if there's any connection.