Great question! 

You can have up to five credit or visa debit cards total for your Neon account.

• To change your card details, head to your My Account via neontv.co.nz/my-account/subscription.
• Enter your password to verify that you are authorised to make changes.
• Head to the 'Subscription and Payment' section of the 'My Account' menu.
• Scroll to the 'Payment Details' section.
• To add a card, click the '+' icon next to 'Add'.
• To remove a card, click the 'x' next to the card you wish to remove.
• To change the default card set for your monthly subscription, check the box next to the desired card under the 'Plan Payments' column.
• To change the default card set for Rentals, check the box next to the desired card under the 'Rentals' column.
• To update card details, select the pencil icon next to the desired card under the 'Edit' column.
• Click 'Save' once you're done!

FYI You can't remove the last credit card from your account.  If you need to replace the default card, add the replacement first, change the defaults, and then you will be able to remove the unwanted one.