Research: Pacific resources
At the moment there are very few specific Pacific websites that are of use when researching US fathers. However, the birth records of the local church or community may be a good place to start.
Pacific interest group: New Zealand Society of Genealogists
The Pacific interest group of the New Zealand Genealogists may be able to assist.
Local churches and government records
The birth records of the local church, or in some cases the country, may have a record of your birth. Unfortunately, while some may mention a US father not many have a name. Nonetheless, it is worth a try.