The best way to check if you can add a payment method is try. You did try and it didn't, so you answered your own question. Apple does not list individual card types or brands -- probably because they are too many and constantly changing.
To see the payment methods that you can use with your Apple ID [account], click here --> Payment methods that you can use with your Apple ID - Apple Support
Note that these are ones that are accepted, but specific kinds (e.g., credit or debit cards) might be required in particular circumstances.
It would also help to know the exact error message you say (ALWAYS include that in posts here). It may be your payment method was declined in your case, not outright rejected. If your payment method is declined in the App Store or iTunes Store - Apple Support
Remember that nobody posting here works for Apple. You know a lot more about this case than we do.