Clematis Carnaby should work for you. I have this clematis. I have it in a planter. Although it has a trellis to climb on, it rarely latches on to the trellis. Instead it rambles from the sides of the pot. See the picture. So in my opinion it should work for you.

Any of the non-vining species will work well for this purpose. That would include cultivars of C. integrifolia, heracleifolia and jouiniana praecox. Even xDurandii makes a stunning groundcover although trainable on a support system.

Sapphire Indigo is marketed as a grounding clematis. Never tried it though.

This can work if you don't have slugs. If you have slugs they will get chewed.

Aluvaboy, I saw your patio planter on here last year and it inspired me to try it this year. It's just newly planted but hopefully in time it will be as lovely and full as yours!