I looked at birth records for Rigneys in Birr (aka Parsontown) by the names you listed--there are several Marys, Margarets, Patricks-- but none of them had the parents' names you gave. I looked in the civil marriage records at irishgenealogy.ie and there were no marriages between a Troy and a Rigney from 1864 to 1890. Are you absolutely sure of the parents' names? Sometimes parents' names on a death record, for instance, are wrong, as they are given by a third party who may have been mistaken. I've also seen a stepparent's name listed as a parent's name on a death record. I hope this is helpful.