If 'doesn't accept' means that you are getting a 'declined' message : If your payment method is declined, or you have a billing issue with a previous purchase in the iTunes Store - Apple Support
Try a different card or see if you can remove item (if you can remove it you should be able to download app updates) : Change or remove your Apple ID payment information in the iTunes Store - Apple Support
If you don't get the 'none' option on the payment details screen : Why can’t I select None when I edit my Apple ID payment information? - Apple Support