You can certainly apply in the usual way but while in New Zealand - online EOI and then submit paper application to the nearest INZ office to where you are staying. However, although I know you have a visa waiver for 3 months as a German citizen, you would have to purchase a return ticket if you do this because the visa-waiver is for people wanting a short holiday or visit before returning to their own country. Without a visa that says you don't need a return ticket, you may well not be allowed to board the flight and even if you did , there is a possibility of being refused entry at the border. You might be able to get a temporary partner visa if you have lived together for three months.