Hi johnkhull41,
Welcome to the Apple Community
Re : I am trying to Edit my Payment Method
If your card-provider has changed too,
you might need to check your new payment method is one that Apple can accept
Payment methods that you can use with your Apple ID – Apple Support
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Re: the site won't let me add the new card
Wondering which site you tried:
Eg: Your Apple ID online account / App Store ? Music / iTunes
NB: You would need to add the new payment method before trying to delete the old card
Try following Apple Support's method (article linked below) to guide you
Change, add, or remove Apple ID payment methods - Apple Support
All the best :-)