Here's a post that might help - https://www.bobvila.com/slideshow/12-ways-to-wake-up-your-tired-outdoor-furniture-47396
Is it the plastic tubing kind or the strap? Either way that might be tricky and it likely won't stick for long. You'd be better off changing the webbing out.
I would scrub them really well first and after it's completely dry, I would use paint intended for vinyl. Maybe with a clear coat over it. I'm not sure how well it will hold up, but, it's worth a try. Spray paint shouldn't cost that much. Or as suggested before, you can replace the material. Honestly, I would clean the heck out of them and add a fabric cover or beach towel to spruce them up, but, that's just me! Good luck and stay safe!
Is it plastic? I would say a spray paint would work best to get all the nooks and crannies on it.
With all the rubbing the vinyl would receive from use, just the up and down action, the paint probably won't hold up very well. I would re-web. Many attractive colors at diy stores and Amazon.
Hello could you possibly post a photograph to better see your situation and woven chair webbing?
Having a visual might be helpful to be able to offer the best guidance .....to a help find the best suggestions or potential solution for your paint question