Hello KN, firstly there are only church records at that remove and not all parishes had records so we are on the backfoot to start with any information found withour further proof, I only found one John father James mother Honora but born in 1827 and baptised 5th February in Mitchelstown, County Cork, mother is Honora Clifford and witnesses are Thomas Sisk and Johanna Supple (both are names even though unusual) the birth of Mary Lynch in 1834 would mean she was only 15 at marriage so I imagine it would be noted on any record.
I again found two Mary Lynch born in 1832, baptised 20th December. Mother was Bridget Mccough or possibly McGeough, witness's were James Rigney and Mary McCough the parish is Newport and the the address area is Cappanaedea, the county is Tipperary and the 2nd Mary Lynch is also a bit odd in that it could be the same one in a different parish, no idea what it going on or it could be a coincidence, the parish is Nenagh, Tipperary and the addres area is Ballynahinch, mother is Bridget McKeogh, witnesse's are again James Rigney and Margaret McKeogh and the baptism is on the 26th December 1832. Newport and Nenagh are not too far apart, there are 3 Ballynahinch townlands in Tipperary, the other one Cappanaedea must be mistranscribbed as it does not come up in a search. YOu can search the Catholic records by year and month here when you locate the correct parish https://registers.nli.ie/
Mitchelstown and these parishes are not too far apart about 30 miles at a guess but they certainly did not meet often if they were them, these are only the records I found so you may not take it as a given, O'Brien is a common name and in that area too. The O prefix was not used a lot from the early 1700s but regained favour in the late 1800s as Irish nationalism awoke a feeling for the traditional names, so some records may be Brien, the name was first used for Brian Boru in the 10th century.
Good Luck
Pat