Is there a way to charge a purchase to the account owners credit card rather than the organizer accounts credit card?
For an "adult" in the family to use their own credit card they would need to be removed.


  Ref: HT201079 Section: near bottom of page, above "*Age may vary by country".


The "adult" could make purchases using gift cards redeemed to their personal iTunes ID, though this won't stop subscriptions or gift purchasing from being charged to the "organizer".


  Ref: HT201079 Section: First paragraph and "Making Purchases".


It's not possible to remove the credit card from the "organizer" account completely, but you could update the "organizer" card to the desired card, then change it back after the purchase. This would only work for non-subscription content. If subscription content is purchased and the card is changed after, the card on the "organizer" account at the time of renewal would be charged. The renewal may also be interrupted. 

Do be careful to prevent any unwanted purchases to the card on the "organizer" account, from any other family members including the "organizer", during any temporary changes.  


  Ref: HT203905 Section: bottom of page "If your part of Family Sharing"



Family purchases and payments
Reasons for not seeing "none" in iTunes Store payment options


Accepted payment card type on "organizer" account may vary depending on 'child' account being present and any accounts with Ask to Buy enabled.