The best way to pay for your client is through PayPal and credit card if they are in New Zealand. As, PayPal is still not available in our country (Bangladesh) and you are not happy with the conversion rate of Western Union, you can try to use Payoneer.
I have billed many times my client through Payoneer and they are residing on New Zealand too. Off-course this can be done when your client agrees to pay via credit card.
Another option is using 2Checkout to bill your client. With 2checkout you can withdraw earnings to your bank account and with Payoneer card too. This also have a catch. You must earn a significant amount, otherwise you will not be happy with all the charges.