No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Us Altitude Reserve, CSP/CSR all have prImary rental insurance I think.
Despite the plethora of brand names, rental companies have consolidated. Enterpise, Hertz, and Avis (and their affiliates) have well over 90% of the car rental market. There aren't a lot of different programs to compare.
Amex Platinum gives status perks and some discounts. Some people like the deals they can get through Costco.
If you want to go with the American Express Premium Car Rental Protection you must enroll your card prior to the rental. The fee is charged to your enrolled card automatically (per rental, not per day).
More info: https://feeservices.americanexpress.com/premium/car-rental-insurance-coverage/home.do
It sounds like the OP isn't looking for recommendations for cards that offer primary or secondary auto insurance, (s)he is looking for a credit card that provides car rental discounts/discount codes.
If you're eligible to join Union Plus their credit card gets I believe 25% off the standard rate at several of the unionized national car rental agencies.