Crunching your request. Won't be long . . .
You can usually ONLY apply for a credit card in New Zealand if you earn 20k or more per annum, so a credit card is usually not an option for most students, but many banks offer overdraft for students with their tertiary debit cards.
This offers the same benefits as a credit card, but usually with the added benefits of no annual fee, 0% interest and no-transaction fees. The down side is that this is usually limited to a credit limit of $1,000 to $2,000.
Some students may be eligible to apply for a standard credit card if they earn 20k or more or if their application is counter signed by an adult with a good credit rating and a steady income. If you choose to apply for a standard credit card, a low interest rate and no-annual fee credit card might be suitable for you.