Can you get a card with a low limit? Say $1,000 - 2,000. Then only use it each month for say up to $50 worth of groceries or gas and be disciplined in paying it off. Don't let the bank or credit union raise the limit.
We have a low limit card for any internet transactions or to use at a gas pump. Works great. They tried to raise the limit on us the first few years (we would get a letter congratulating us) but we said no.
by the way, our credit union offers a 1.5% cash back card which we use to get occasional grocery or gas gift cards.