Unlike the tombstone for his wife, Margaret, Patrick Greene’s tombstone does not contain his birthplace in Ireland. Naturalization records, land records, obituary, death record only give the location as Ireland. The puzzle was solved when I located an obituary for his brother, John Greene, who died 20 March, 1923 in Westgate, Iowa. That gave the town as Ballingarry, County Limerick, Ireland. Further investigation identifies the parents as Robert Greene and Mary Kelly.
I found the marriage record for Robert and Mary at The Irish Family History Foundation website, 16 February 1836, also in Ballingary. Unfortunately, that date represents the very earliest Catholic church records … so this may be the end of the line for now. Nobody ever guaranteed Irish research would be easy. But, oh, just to find a “bit”more!