I would say the best credit card for groceries & grocery stores would be the Chase Freedom Rewards credit card. I would rank that card as the next best after the Amex Blue Cash
since as you mentioned that one doesn't work for you. While the chase doesn't give you the 5% cash back as the Amex does, it does give you 3% in your top 3 categories. Those categories include things such as groceries, gas, fast food and others. Which three of those categories you spend the most in, you will get 3% reward points for which equals 3% cashback if redeemed in the form of a check. For all other categories I believe it gives 1% cashback. Although this is not the 5% offered by the other card above, it is clearly the second best option currently on the market.