When FS is set up the organizer must enter a payment method. This is automatically applied to any family group member should they have insufficient personal balance to pay for items. As such your CC profile is actually linked to their accounts. Under FS they can't have their own payment methods other than personal balance. In that regard there is nothing for them to set up under their payments and in fact they can't set up a payment method. Your payment method you set up on your account should automatically work for them too. This is outlined in How to share purchases with your family - Apple Support
It is possible that the error message is just reflecting an error from your payment method and you may wish to check your card and make sure it is still working: Add a payment method to your Apple ID - Apple Support
If you don't see an issue then the error message you received is one of those obscure ones that may require somebody from Apple to decipher:
Contact Apple. Click here --> Choose your country or region - Official Apple Support Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.
or:
Contact Apple for support and service --> "See a list of Apple phone numbers around the world."
Click here --> Contact Apple for support and service - Apple Support
