NZ only operates flights from AKL - PPT a couple of times a week (NZ and Air Tahiti also have a codeshare on that route).
According to their timetable NZ operated flights take place:
AKL-PPT on Sundays and Fridays
PPT-AKL on Thursdays, Fridays and Saturdays
Was successful doing the following sample booking:
AKL-PPT Friday, Feb. 12
PPT-AKL Friday, Feb. 19