As a father-son interview in the Irish Independent from 2008 makes clear,

the generations of Fureys are:
Ted Furey and the Grandmother in question, Ted's wife Nora.

Ted and Nora's sons
Finbar, Eddie, Paul, and George, The Fureys.

Finbar, with his wife Sheila, parented these children:
Martin, Aine, Robert, Katriona,
and their youngest, Finbar,
referred to by Finbar Senior as 'Plan B'. (see interview)

Martin and his wife Jane raised their family in Kilkenny:
Hannah and Culan (as of 2008).