If you see an error that says
Sorry, you are not eligible for this offer. This offer cannot be used with your current payment method.
It means that your current billing method prohibits applying a promotional offer or Gift Card to your account.
If you are billed by iTunes:
You can either apply the promotion or Gift Card to a different or new Netflix account, or you can cancel your existing account, wait for it to fully close at the end of your billing cycle, and then restart the account with the promotion or Gift Card.
If you have Netflix through a Netflix-included package:
You can apply this promotion or Gift Card to a different or new Netflix account.