You could try
www.charterguide.co.nz, which is a collection of private owners who charter thier boats. There are very tight restrictions on chartering boats in NZ which set standards for the boats and restrict the cruising limits. You can usually
cruise from
Auckland to Bay of islands and back but the other areas are limited to those cruising grounds.
Tonga ia well worth a sialing visit even if you have to hire from
Mooring. I have sailed there 6 times and just love it. No one really
sails Tonga/New Zealand for fun though. Its a hard slog with nothing between you and
South Africa or you and
South America at times. I can't imagine anyone
renting you a private yacht for that trip.
Particularly if you have
kids I would recommend chartering a yacht in Tonga, Whitsundays in
Australia and Hauraki /bay of islands. I recommend Fairwinds in the Bay of Islands. Perhaps combine that with a campervan tour of NZ.
The whitsundays are really lovely, beautiful
anchorages and great snorkelling. I am going there in 10 days time.