My ancestor Luke was a son of Francis, who held a five acre and seven acre farm at Lisphillip West, and a forty acre farm at Runnacocka in 1824, recorded in the Tithe Applotments, where a John Dempsey, probably brother or father of his wife Brigid, held a twelve acre farm on each of those townlands as well, both are in Kilmacumsy, where the father of Francis, John and grandfather Patrick signed the 1792 proclamation of the O'Conor Don, agitating for Catholic rights. Patrick was recorded there in the 1749 Census of Elphin. He was the son of John Conry, who was noted as a skilled antiquary by my great-grandfather's grandfather Charles Henry O'Neill, who wrote that he compiled the pedigree of our ancestor Con Modera O'Neill, who had fought at the Boyne like his father, and whose mother was the sister of Sir Niall O'Neill, Rose. John Conry was the son of Peter Conry, who wrote several poems for Tadhg O'Roddy, and was himself Ollamh of Fenagh, and Anne O'Conor, the daughter of Cathal Oge O'Conor Don. Peter Conry was the son of Fearfeasa, of Four Masters fame, who was a second or third cousin of Flaithri O'Maolchonaire, Archibishop of Tuam ; the family tree can be seen, I hear, in Paul Walsh's Irish Men of Learning, altough I have seen only Benjamin Hazard's version of it, which may or may not be significantly edited/expanded upon.
So to respond to Michael King, I believe Sir John Conroy claimed descend from a nephew of Flaithri, Muirghuis, and we do share some degree of relation, but their pedigree has been questioned by Irish antiquaries for many years, some of whom believe it to be a work of fiction, others unverifiable.
http://titheapplotmentbooks.nationalarchives.ie/reels/tab//004587462/00…