Carmody received his primary education at a local national school in Ireland, then attended St. Brendan's Seminary in Killarney, Ireland for his high school education. After finishing at St. Brendan's, he entered the Major Seminary of St. Patrick in Carlow, Ireland, for his priestly formation .
Carmody's early education took place at a local Irish national school before attending St. Brendan's Seminary in Killarney for his secondary studies. He then went on to the Major Seminary of St. Patrick in Carlow, Ireland, where he received priestly training.