Credit-card with cash-back, flexible online payment?

 I'm looking for a cash-back VISA card whose balance I can
pay (1) from my existing bank account (2) through a decent
web interface. No annual fee. I don't care about APR. I'm
hoping for 1% back on pretty much all purchases.

Reason for asking: My perfectly good card got taken over by
BankAmerica, whose web page apparently won't let me pay
online unless I open an account with them. I long for the
Visa equivalent of a Discover card: Discover makes it
perfectly easy (and free) for me to pay my balance by
entering various numbers from the bottoms of my checks.
(But, alas, Discover is not universally accepted.)  Normal
online shopping for credit cards doesn't work because you
don't get to see the "make a payment" web page until you
have the card.

If you have a card that sounds like what I want, please
let me know the issuing bank or the web site where you
go to make payments. Thanks.

--
To email me, substitute nowhere->spamcop, invalid->net.