You can do so by going to my secure website at https://secure.mychurchwebsite.com/client and login with your email and pass.
Note: If you do not know your password, click on the 'forgot passwork' link on that page. If you do not know the email on file, please contact us at www.mychurchwebsite.com/support.html
Once logged in, go to CLIENT INFO>PROFILE and at the bottom, under 'billing information' subheading, you can see where you can update the credit card. Just delete the card there and update with the new one.