Good Morning
Apologies for the delay in replying to your message.
As Patrick was born after 1864 you should be able to obtain a civil record of his birth and perhas a civil marriage record for his parents. Have you checked the following sites?
www.familysearch.org has a huge database of genealogical records including some church records for Ireland.
www.rootsireland.ie have a large collection of Irish Church records, however you have to pay to use this site.
It may be difficult to find information without a more specific place of origin. Most Irish record sources- church records, land records, census records- are based on specific locations. Until you know a specific location within Ireland, preferably a parish or placename, it may be difficult to do anything more with these records.
You could also check the Tithe Applotment Books 1823-1837 and Griffith's Valuation 1847-1864:
http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
http://www.askaboutireland.ie/griffith-valuation/
The website of the Ulster Historical Foundation is also very good: http://www.ancestryireland.com/
Remember to post any new information that you find here. The more information you post, the more likely it is that one of our volunteers will be able to advise or assist you. Also include information concerning which sources you may have already used so others may further your search.
Best of luck with your search
Clare Doyle
Genealogy Support