How to change payment method?

I created an Apple ID for my son about 6 mounths ago with a digital prepaid visa ecard. To control perchrses and prevent him buying Inappropriate I buy him gift cards with adequate amount of money anytime he wants to perchase new apps.
Now the card is expired and I want to continue with gift card paying method, but I can't change the payment method to "none". He is 9 years old and I don't want to use either my credit card or another prepaid one. Is it a way to solve this problem?!...Thanks.