John A Leary/O'leary

My great-grandmmother was Mary Catherine O'Leary, born in Chicago in 1875. Her father was John O'Leary who was born in Ireland. I can find no records except for some Chicago records so any clues I have of his origins are mostly family lore and because my grandmother was estranged from her mother (Mary Catherine O'Leary) she was reticent about talking about her mother or any of the O'Leary family. Figuring out John's birth year from his death records I pin it at 1853. There was some talk of him coming from County Cork, but it may have been County Kerry. My best bet is finding any relative that would have talked of a brother, cousin, or some other relative named John Leary/O'Leary who settled in Chicago. This John O'Leary married Deborah Dinan in Chicago in 1874 (I think). I have taken two different DNA tests but since this is my mother's ancestor I am three females removed from John O'Leary and his Y-gene. My only real hope is someone else's family lore. I have not found when John entered the US since it did not show up in port records.