Martin / Mary Hartigan - family information please

Hello, I am interested in finding the origins of my Ireland ancestors to research further. I do not know where to start. There is no one left to ask and the documents found only state, born in Ireland.

Martin Hartigan - tombstone shows birth year 1801 death year 1871

Found Buffalo New York newspaper death notice Oct 29, 1871 age 58 yrs

Per City of Buffalo New York no death certificate found

Mary Hartigan - tombstone shows birth year 1829 death year 1910

Found Buffalo New York newspaper death notice April 3, 1910

Per death certificate DOB May 14, 1840 Ireland DOD Apr 3, 1910 Buffalo, NY

Father Jno Hartigan Ireland Mother Dont know Ireland

Initially thought Martin was Marys father but realized he may be brother after DC received and article stating Martins funeral from the residence of his brotherinlaw, Christopher Farrell (spouse of Mary Hartigan).

Any county and/or parish information or additional information found on the family, would be appreciated. Thank you, Chris Kraffert