there is a special paint for cement- local big box diy is where I found it. my back patio ..I painted a rug on it.
Yes - I got my cement paint at a Michael's store, so thinking crafty places would have it. We painted various size circles on our front porch. Warning: it doesn't weather really well if it is totally exposed to sun and rain, but it lasted for a few years and got many compliments!
Here's how one of the DIY bloggers I found painted her concrete floor to look like tile, you could definitely put your own spin on it for your patio https://farmfreshvintagefinds.com/barn-makeover-stain-concrete-part-2/