DNA would be my suggestion. Check out the Coffey Surname YDNA project to see the different Coffey lines that have been identified. Have a male Coffey cousin take a 67 marker YDNA test and join the project. Fred Coffey is wonderful at helping new members. He has been able to identify at least 3 distinct groups of Coffeys in America--the Edward Group, the Peter Group, and the Hugh Group. Also check out the Coffey Cousins Clearinghouse website and contact Jack Coffey, the editor, with information on your family. He can post your query in the next quarterly newsletter and advise you if he knows of any New Zealand Coffeys already.