This thread goes beyond discussing only the Cumulus credit card and provides some good and recent advice on other cards too.
EDIT: The Poinz credit cards seem to mirror the Cashback card duo (1% Amex, 0.25% Visa) and they’re issued by the same issuer, Swisscard AECS. I know at least a couple of restaurants that have recently stopped accepting AMEX though.
Certo One provides 1% cashback on a Mastercard with three merchants of your choice (from about 20). But keep in mind that Denner, Migros, Coop and SBB - which arguably receive most of the day-to-day spend for many households - will accept AMEX just as well.
I’m applying for the IKEA Family credit card at the moment, which has 100 CHF sign-up bonus offer until the end of the year and (effectively) 1% cashback - paid in IKEA points/gift cards. I can surely find something to replace / buy for my household at good price at IKEA, if not eat at their restaurants. Additionally, forum member @Daniel made me aware that the card seems to have quite good insurance benefits (for a card without annual or monthly fees).
Finally, the new Cumulus credit card issued by Migros Bank seems an excellent choice as a “all-around” card for people who want to keep their “card portfolio” simple and not juggle around multiple cards but still get some bonus on their turnover.