Hello Jacqueline
There are Gaffneys in New Zealand. My great grandparents are Thomas Gaffney and Susan Foley. They married in 1836 in Duffield,Derbyshire,England. and subsequently lived in Belper, Derbyshire. Susan came from Dublin. I do not yet know where Thomas came from in Ireland. Their 3 children all came out to New Zealand starting in 1859 and used the spelling Gaffaney
This maybe of some use ,rather belatedly
Michael Gaffaney