NZ doesn't have any rivers that are long by US standards. Between the rocky gorges, one encounters braids and shingle beds, which can be frustrating at lower flows (the height of summer might not be the best time to try). Best bets for summer are rivers with sources in snowfields and glaciers. Otherwise, be prepared to track the rainfall.
For multi-day raft trips on South Island, the Buller River & tributaries probably offer the most possibilities as far as dependable flows, multi-day runs, and whitewater (NZ IV). You might also look at the Grey River and tributaries, which reaches the sea at Greymouth where there are several good pubs. On the east coast, check out the Clarence River which reaches the sea near Kaikoura (great spot to end a trip with kai moana and wine).
On North Island, the Whanganui is a wildly popular scenic trip with rental boats likely available. For a look at the river, check out the NZ film River Queen
: River Queen (2005)
There are lots of whitewater runs (e.g.
the Karangahake Gorge on the Ohinemuri River), but it's harder to find multi-day camping trips with whitewater. There are also lesser known rivers with road access and potential for overnight raft trips, such as the Waioeka above Tauranga on the east coast:
Gorgeous, and typical of the region, with (as I recall) moderate whitewater, and public road access. This is a midwinter photo. Probably much less flow in summer.
Given the camping gear, etc. needed for multi-day raft trips, it might make sense to use duckies and concentrate on day runs. Keep the boats rolled in the boot of the rental car. Hitchhike the shuttle, eat pub food, and sleep in a real bed.
Same rivers. Simpler approach.
If you do the small-boat thing, check out the Pelorus River (between Picton and Nelson) and stay at The Trout
in Canvastown, a workingman's roadhouse. The rooms are tiny, the pub food is good, and the brekkies are monumental.
If you're renting boats, do some coasting in sea kayaksó if you're not familiar with tide tables, coastal currents, and such, study up. The rivers are beauts, but the ocean is magnificent.
I'm aching with envy, mate. Wish it was me going.