All car rental companies in New Zealand require the deposit to be paid using the renter's own credit card. This is especially important if your spouse manages the finances. Apparently, this requirement is mandated by New Zealand law, a rather perplexing regulation.
AVIS accepts the renter's electronic driver's license (accessible through the 12123 app) plus a certified translation in place of a physical license and translation, but still requires the renter's own credit card, making it relatively more accommodating.
Some rental companies will promote a "worry-free fuel return" service, which essentially means paying for a full tank of gas in advance at a relatively low price. If you are aware of your fuel consumption (but in reality, you don't know what kind of car you'll be assigned until the paperwork is complete) and can ensure the tank is almost empty when returning the car, you can consider this option. Otherwise, it's strongly discouraged; returning the car with a full tank is sufficient.
For long-distance trips, it's recommended to purchase full insurance from the rental company, covering tires and glass. During a trip of ten days or more on the South Island, you'll almost always encounter stones hitting your windshield.
If returning the car at the same location, mark the pick-up location on a map, as it's easy to get lost when returning it (for example, I wandered around the airport several times).
There are many more customers renting EZI than AVIS.