McCaffrey

I am desperate for some help in research my irish ancestor Patrick Caffrey born about 1802, maybe Monaghan County. Immigrated to Pennsylvania in 1825 where he became a weaver. He states in in statement of aliens that he was from Monaghan, couldn't write his name but it was spelt Caffry. Family says he dropped the Mc coming over here and also his Catholic religion. He died in 1850 so most relatives didn't have anything to say about him. My family is the only living relatives.
My problem is that I am visiting Ireland for the first time Sept 11 and had hopes of doing research on my Patrick but as I have researched on the internet I am realizing this might not be easy. I thought I would just visit Parish church and look at their records but find out they don't go that early.
I also found out that McCaffrey or Caffrey is a really common name in Ireland. I have collected every McCaffrey I can on what records are available but can't make any common link. Between Tithe Applotment  and Griffith valuation they don't seem to stay in the same townland. I would love to know what else I can do while I am there and wonder if you can help me with this.
I have been communicating with the Clogher Historical Society in Monaghan and they don't think they can be of any help.

Also would love to communicate with others working on the McCaffrey Lines in Fermanagh or Monaghan Counties.