I have the Qantas Diners Card for this reason, but you will pay in some form or another.
I only use my Diners for
Wednesday night dining 3 point per dollar
other than that it everything goes on the Amex and then if they don't take Amex I put it on the visa..
When its comes around for renewal I will ask to cancel the card for I don't see the cost benefit to see if I can reduce the annual fee!!