Depends (no pun intended) where in the country you are. I'm in Auckland, and there are plenty of options:
Nappies for Less - Baby Online - Nappies & Baby Gear and Nappy House - Disposable Nappies Online, Baby Products & Baby Gear > Babies NZ are both chains with lots of stores in Auckland.
Sanicare/Bunzl (based in Onehunga) are the NZ distributers for Abenas. They normally only sell wholesale, but will sell to the public provided you buy by the carton.
Trade Me is always a good source, there are a number of sellers who stock adult nappies.
Otherwise, you should be able to pick up Drynites (Goodnites) from any supermarket.