There are many 2nd and 3rd tier rental car companies in NZ. Some are at airports. They rent out used Japanese cars. NZ imports 1000's of used Japanese cars (+5 years plus old)
https://www.acerentalcars.co.nz
http://www.apexrentals.co.nz/
http://www.omegarentalcars.com/
https://www.jucy.co.nz/
http://www.a2b-car-rental.co.nz/ (I have rented from these)