Any of the larger known brokers in NZ do allow US option trading. I would pickup the phone and call them on the specifics.

In my previous posts, my stance is not to imply NZ residents can not trade overseas / US derivatives. There are many to choose in NZ but the coming of the FME created regulations which favoured the NZ brokers to provide such services than the NZ investor having 'choice' of sending their $ abroad and do such trades directly. It's a form of protectionism racket.