Hi,
It will be a little tough tracing John Gibbons, as those are common names in Mayo. Have you completely exhausted your research in the US? Have you been able to find death certificates for John James or Thomas Patrick? Usually death certificants can contain parent names, and if you have the mother's surname, that can help narrow down the search area.
Another trick is to see if you can find any church records. If Owen Gibbons had any children in Kentucky, finding out godparents names might indicate some family connections; same if John James Gibbons had any other children in Kentucky as well. For me, my ancestors settled in Scranton, PA and I have been able to get marriage and baptismal information by contacting the churches in the area.
I have a Margaret Gibbons McNally Geraughty, b 1824 in my tree - luckily I found her death certificate and it indicated her parents were Thomas Gibbons & Jennie Connolloy. I found a Thomas & Mary Gibbons from Mayo living in Scranton PA, where Margaret settled, so that formed a weak connection. Then I noticed a family tradition of naming girls Mary Jane, but calling them Jennie, so that was another clue. Finally, I found a baptismal record for one of Margaret's grandaughters with a Mary Gibbons listed as a sponsor, so this was more evidence in establishing family linkages. Sometimes, you just need to find whatever you can ....
Let us know if you have any luck!
John
