This is a kind of
holiday let but is also used for business people by the sound of it because it's close to the city centre. I wonder if they'd do a special deal for you as NZ is about to come out of the peak holiday season and you appear to need somewhere long term. It's currently advertised at $90 per night if you take it a month at a time.
Then there's
this one where they say a longer rental will reduced the rent.
Another one .
There are a few other possibles on this site but they seem to be booked up around the time you would arrive.
You could look at
Green Gables Hotel or
INNZ travel office or
Accommodation NZ ..
I have no personal knowledge of any of these places so care would need to be taken to ensure that they are what you're looking for. Some rental places can be pretty dire. I'd hope that a few members will have more inside info to offer when they get a chance to look in on the forum.