Punk was and still is pretty popular in New Zealand, there have been many bands over the years mostly on the underground scene but a few have been a bit more widely received. It's pretty hard to make it mainstream at the best of times and if you add to that a very small country with a limited fan base and you can see the obstacles that face many alternative bands from New Zealand.
One band that did pretty well is Kitsch - (note there are a few bands in the world with this name), they are a Punk band from New Zealand and have been around for over fifteen years - on and off. They play the more melodic punk and have released a couple of albums over the years, they have also supported many international bands like NOFX and Bad Religion to name just a few.
Kitsch - Stay Right Here