He became Apostolic Nuncio to New Zealand, Tonga, the Marshall Islands, and Samoa, and Apostolic Delegate for Oceania on 27 April 1996. His remit was expanded to include Apostolic Nuncio to Fiji, Kiribati, the Federated States of Micronesia, and Vanuatu on 15 October 1996, and Apostolic Nuncio to Nauru on 7 December 1996. He was also named apostolic nuncio to the Cook Islands and Palau on 14 July 2001. As the longest-serving resident diplomatic representative to New Zealand, Archbishop Coveney served for a time as Dean of the Diplomatic Corps. While based in Wellington, he also represented the Holy See at the inauguration of Chen Shui-bian as president of the Republic of China (Taiwan) on 18 May 2004.