Hi. I might be able to help here. At this moment in time i have nothinbg to add but my father and grandfather were both Falvey's, Born and bred in Cork. Unfotunately i did not spot my grandfathers name as one of the 7 children listed as his name was Eamon or better known as "Ned". My father also shared the same name. "Eamon John Falvey" born 1954.
I will see if I can find any information which could help.
Sean Robert Falvey.