As yet there is no centre in Fermanagh, but there are plans afoot. Depending upon what you want to do I may be able to make suggestions. I can say from experience that you would probably learn more at the PRONI in Belfast that you will in Fermanagh.
Searching my Graham roots threw up thousands of them in Fermanagh and like yourself the problem was to identify one single individual from all the others of the same name. I wish I could offer something positive but unless you have a 100% accurate date of birth the chances of identifying him are slim to none. I saw the tree on Ancestry and the d/o/b came from USA census records. Some individuals did know their own d/o/b but most simply guessed and probably kept the guess as their d/o/b in USA. When asked by an official when were you born, no one would want to look stupid, so they would almost certainly make up a date.
I thought US death certificates included parents names. Did he leave a will?
From the names I am guessing that Tierney would be RC. My experiences have been with Protestant Church records so I can't advise much on them. I do have contacts who may do.
It did take over 30 years to locate my family in Fermanagh, but what I found did not take me back any further. I have been up many a blind alley in my time so I can hopefully save you some wasted effort. The tendency is to go the location your family came from, as I did, rather than go where the records are - Belfast or Dublin. Church records from the time you want if they still exist are in the PRONI either as originals or on microfilm. Local Fermanagh Churches may have more recent records, and many have transcripts of the originals, but as always transcripts are prone to errors.
You could have a look at the Fermanagh Gold website as a lot of records have been donated and stored there. You need to be a member of the Fermanagh Gold mailing list but that is simply a matter of subscribing. It is one of the best mailing lists with a very active and knowledgeable membership, some of whom live local.
http://lists.rootsweb.ancestry.com/index/intl/NIR/FERMANAGH-GOLD.html
I did find one Kearns USA connection.
http://applications.proni.gov.uk/DCAL_PRONI_WillsCalendar/WillsSearchImage.aspx?id=227051
Bob Graham(County Fermanagh XO)