I cannot for the life of me understand why you believe George was born in Ireland. His WWI draft card shows him as a natural born citizen. The 1930 census of North Pellham, Westchester Co., NY shows he was born in New York. Mary was born in Pennsylvania and her parents in Scotland and N. Ireland.
I did find a George in the 1920 census living by himself in Pelham despite the fact he was married. He was born in NY, his father in GA and his mother in NY so it may not be the right George. I could not find Mary and the children.
The 1910 census shows George and Mary with son George living in New York City. They were married three years. He was born in NY and his parents in England and Ireland. She was born in PA and her parents were born in GA and Ireland.
The 1900 census of Manhattan shows Geo. R. Gannon, born Feb 1881 in NY, as the son of Thos R., born Mar 1831 in England, and Ellen, born Aug 1844 in Ireland. He immigrated in 1865 and she in 1849. They ran some sort of boarding house. However, the 1880 census shows Thomas born ca 1840.
Most likely George and Mary married in NYC. Check with the NYC Archives about getting a copy of the license. Hopefully it will have data on their parents. Aside from that it will be necessary to find out when and where George died in order to get his death certificate and obituary. Both of which should clear up the matter of where he was born and who his parents were. I would imagine Mary is buried with him. Hopefully she has a tombstone and her dates of birth and death are indicated. The cemetery office might have some helpful data.
If the Thomas I found who died in 1906 is the correct father for George I suggest getting his death certificate. It should have his parents and where he is buried. Ellen is probably buried with him unless she remarried. Their obits may prove helpful and the NYC Archives probably has other records that could help. I haven't been there myself, but I understand the New York City Public Library is helpful in doing genealogical research. Since they were Catholic check with the New York Archdiocese. They probably have an archives which could be helpful in tracking down church records.