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I wasn't able to find a baptism record for Philip Martin but rootsireland.ie does show a baptism for a Patrick Martin born to a father Terence Martin and a mother first name Bridget (last name not recorded) in the parish of Booterstown/Blackrock Dublin in 1822. I couldn't see a marriage record for Terence and Bridget. Other children include: Anne & James, 1819; Patrick (above); John, 1815 and Laurence, 1813.
There is also a baptism record for a Terence in the same parish in Jan 1785, obviously the Terence above. His parents were recorded as William Martin and Ann (surname not recorded).
Can I ask why you think Philip was born/baptised in Fermanagh. Could the above family be your ancestors, there are some similarities?
I see that that were still Martin listings in Caste Coole in the 1901 Census, I wonder if some are related?
http://www.census.nationalarchives.ie/search/results.jsp?census_year=19…
Let me know what you think
Best wishes
Clare Doyle
Genealogy Support