You could recover it or have it recovered. You could also paint it. Amy Howard has great tutorials on how to paint fabric. https://www.amyhowardhome.com/blogs/how-to-do/painted-chair-and-fabric-cushion
We actually replaced the slings with new ones. You can order them online and install them yourself. It works especially well if your slings are worm or torn...but it's definitely more labor intensive and more expensive than painting them. Here's my DIY if you want to peek. https://www.exquisitelyunremarkable.com/2017/07/how-to-replace-patio-furniture-slings.html
I appreciate the information, but I was hoping to get information on how to paint the sling fabric and not the frame. Thank you.