There is a special paint made especially for plastic. Maybe that would work?

You can buy spray paint for outdoor plastics, but honestly, plastic outdoor chairs are cheap, I'd just buy new ones.

Go to the paint section at Home Depot, Lowes, or even Walmart
and look at spray paint. There they will have outdoor paint, it says it on the label. The cap is textured and the color, its usualy rough. Buy it , go home and on a nice day clean the chairs up the paint. GOOD AS NEW !! GOOD LUCK

Sand of loose stuf and paint with Crylon fusion sold by Canadian tire Been there done that