Francis (Frank) McCarthy

Hi, hope someone can help with this vague question. My wife's Great Great Grandfather is John McCarthy. He was probably born around 1820 seeing as his son Frank McCarthy was born about 1856. John's wife is Bridget (nee Fulton). Son Frank migrated to Australia & New Zealand after initially commencing in the priesthood at home though family believe he was training was cancelled at some stage possibly due to unsuitability. Frank co-habited & possibly married Annie Kenny on 15/5/1892 in either Ireland or Australia. If I could find birth or death records for John & Bridget that could link me to their County that would be most helpful. I have created a Wikitree account for Frank (McCarthy-3979). Any help at all is much appreciated as Franks recorded details so far have been very contradictory! Frank & Annie's marriage dissolved around 1913 & Frank died in New South Wales, Australia in 1925. Some family believe he may have migrated to New South Wales via America & / or New Zealand. He was not known to be keen on official records such as birth registration for most of his children.