Cain was born in 1837. He was the son of Timothy O Mahony and Margaret Cronin. He passed away about 1901.[1]
Birth and moving to the states https://www.familysearch.org/ark:/61903/1:1:QPKJ-G7QM "New York, County Naturalization Records, 1791-1980," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QPKJ-G7QM : 9 September 2019), Cain Mahony, 1884; citing Naturalization, Clinton, New York, United States, citing multiple County Clerk offices of New York; FHL microfilm 005411178.
I have been working on finding my DNA link to your Sylvester O'Mahony and the Poulagour O'Mahony group.