judging by information here, you cannot change payment method while you're family member:
Manage payment methods that family members use
When you set up Family Sharing and turn on purchase sharing, one adult in the family—the family organizer—controls a single shared payment method for everyone in the family group. Learn more about family purchases and payments.
If you're the family organizer, you can add multiple payment methods to your own Apple ID, but your family members can use only the first payment method in the list. If a family member can't make a purchase, the family organizer can move a different payment method to the top of the list.