"AutoEurope does not take Diner's" "Want it for the insurance"

The only difference between Diner's and VISA/Mastercard is the primary CDW coverage. It really makes no difference in Europe because your U.S. or Canadian insurance company does not cover you in Europe. Therefore the card company is primary. If you have an accident in Europe, the chance of your domestic insurance company learning about it is practically nil, unless you personally call them and tell them.

I had an accident in Italy, (somewhat different because Italy requires you to buy CDW) on an AutoEurope rental and it was absolutely painless in terms of claims resolution. Basically, I turned in the car and walked away. Whether Diner's or one of the other cards is used makes no difference.