The use of a credit card is a GoDaddy requirement, and part of their ToS for those respective codes. There is no way to circumvent this requirement. However, a Paypal Master Card will work fine. It's used just like a regular bank issued debit or credit card, but is issued by Paypal, and will only pull funds direct from your personal Paypal account.
It's free and quick to get one, but may require a simple upgrade to your Paypal account, depending upon your account level. Simply call Paypal, or visit your Paypal account, to learn more.