When we went to NZ a few years ago we were recommended to Apex rent a car. We picked it up in Auckland and kept it for just over a week while we went up to the north and back. Then we flew to Christchurch took the train a day or two later to Greymouth and picked up another car. That one developed a gearbox problem and we swapped it in Christchurch (not a major issue in any sense). Eventually we took it on the ferry back to the North Island and finally dropped it in Auckland. We were in New Zealand for about 2 months and only had about a week without a car. Apex treated both rentals as one and charged us as if it was one 50 something day hire. Oh, and they threw in the ferry ticket between the Islands "free".
There are several companies hiring out campers. These are mainly the sort of thing we see on the roads in the UK - van chassis with a camper body. However, a couple were hiring Toyota Previa which they had modified by stripping out the back seats, fitting a bed and (not sure how) a two burner cooker. Not sure I'd want to sleep in one but in terms of economy a good deal and the campsites we saw all looked good.