I might be able to help you a little bit,
Im aware that my grandmother Martha Hay Glass of glengarnock had a cousin called bessie falloon/fallon who was of irish descent same as my family. I can recall meeting her when I was a child. My grandmother also referred to the "hamiltons" as cousins. I knew margaret Hamilton,
I rather suspect Bessie was a cousin on the "Hay" side of the family (mothers) rather than the "glass" side. I also suspect she was a second cousin. Anyway, she married a man with the surname "Hall" whom my father always said were "cousins". At least one of them should still be around. They all lived in Beith. Glengarnock is split into four parishes so when checking records its important you follow up links for beith kilbirnie dalry and barkip as well as the parish of glengarnock.
I am aware of another Fallon family who are catholic living in the area, but I really dont feel you are referring to catholic families here as my family were all very very staunchly presbyterian at that time.
Hope that helps a bit.
Joseph
