Fidelity Investments offers an American Express Gold or Platinum card, although you have to sign up for Membership Rewards program separately and pay the fee.
It's a mix between a debit card and an AMEX card (looks like a regular AMEX gold/platinum card, except with a Fidelity logo just under 'American Express'). You make charges, and it will deduct them from your bank account automatically at the end of the month--no bills to worry about.
Only stipulation is that your balance cannot fall below $5,000 in the account that is tied to your AMEX card.
Just another option...
Cheers,
Lawrence