He was born in Dover Street, Belfast on 22 January 1913 and baptised in St. Peter's Pro-Cathedral. He was the eldest of nine children. His father, Patrick Conway was a house painter and ran a paint shop near Royal Avenue while his mother, Annie Donnolly, came from Carlingford in Co. Louth. He attended Boundary St Primary School, St Mary's CBS (now St Marys CBGS Belfast), Queen's University, Belfast; St. Patrick's College, Maynooth; Pontifical Gregorian University, Rome. He emerged with a doctorate in Canon Law summa cum laude tieing for a gold medal with a German Jesuit.