|Reference style||The Most Reverend|
Coveney was born in Tracton, County Cork, Ireland, and was ordained, aged twenty-four, as a priest on 21 February 1959 by Cardinal Luigi Traglia. After doing parish work in England and teaching in Cork, he went in September 1966 to work in the English-language section of the Secretariat of State in the Vatican.
On 27 July 1985 he was appointed titular Archbishop of Satrianum and Apostolic Pro-Nuncio to Zimbabwe and Apostolic Delegate to Mozambique, and ordained to the episcopate on 15 September 1985. The Principal Consecrator was Cardinal Agostino Casaroli; the Principal Co-Consecrators were Archbishop Gaetano Alibrandi and Bishop Michael Murphy who was the Bishop of Cork and Ross.
He became Nuncio to New Zealand, Samoa, Tonga, and the Marshall Islands on 27 April 1996. His remit was expanded to include Fiji, Kiribati, the Federated States of Micronesia, Vanuatu, and Nauru later that year, and to include the Cook Islands and Palau in 2001. As the longest-serving diplomatic representative to New Zealand, Archbishop Coveney served for a time as Dean of the Diplomatic Corps. He was then appointed Nuncio to Greece in 2005. He retired in 2009, and was replaced by Archbishop Luigi Gatti.