Disney requires a direct withdrawal from a bank for their AutoPay, which is required if you want to drop the interest rate. You can use a credit card for any additional payments outside this AutoPay.
If you pay a higher interest rate, and don't have AutoPay, I'm not sure.
They pretty much force you into AutoPay using a checking account. However, you can pay your principal down with your Disney Visa and collect points. I'm not sure it's at the 2% reward rate though as I've never tried.