I’d like to add new payment method and it is not allowing me

What happens when you try to add the new payment method? Error message(s)? More information would help.

See the Apple Support articles below which has some things you can try to fix the problem. Link to contact Apple Support in the article. 

Apple ID payment information - If your payment method is declined, or you have a billing issue with a previous purchase in the iTunes Store*

Possible fixes.   Fix ‘Your Payment Method Was Declined’ Error In App Store.  -

                          Payment method declined in iTunes or the App Store.   -

Apple ID payment information - change.  *

If you need to change or update your Apple ID payment method.  *

If necessary, contact iTunes Support for assistance. See the Apple Support articles below for contact information.   

iTunes Support – world wide   -

Apple Support schedule phone call     -

Billings and Subscriptions   -

If necessary, use Twitter or Messages.

Apple on Twitter

Messages chat with Apple