I agree with this being probably the best DIY, you can get 100% as good as factory IF you do all the prep right. Also the 2K clear - Full painters suit with hood, googles, respirator and gloves. Don't get it on your skin, in your eyes and if you get it in your lungs or any person/animal near you, bye bye. I have used it at home under a tarp spray booth after sending the wife, kids and pets for ice cream to keep them safe. After it is sprayed and kicked you're fine to remove all the PPE and let folks back near. Only nasty while airborne for like 5-10 min.If you just want a "patch job", then I'd advise wet sanding it with 3000 grit until the edges of the pealed away clear coat are pretty much flush with the base color. Or if you pealed away the loose paint, could use compound on it instead to try and not hurt the base paint during the process. Then afterwards apply some 2k Clear Coat, a nice wax or ceramic coating related product.
If you want to do it properly, you'll need to remove the spoiler, then you'll need to strip all the paint off, find a matching base coat color for your vehicle at your local auto-parts store, and a suitable primer. Then after thorough cleaning with alcohol and allowing it to flash off, spray the primer on in very thin and even coats to avoid "runs". Better to make 5-7 light passes, than 2-3 thick coats, as your more likely to have runs. Then repeat with your base color, and again with the clear. If you do it improperly and get "runs", let it dry thoroughly, then use sandpaper to remove it till it blends in with the rest of the paint (which you'll want to scuff up with that same grit sandpaper). Then resume applying the thin coats as necessary. Once your done applying all the clear coats, would advise wet sanding with 3k or higher grit sandpaper to remove any "orange peel", then buff it out with some compound/polish, and then apply a ceramic coating of some sort, such as Turtle Wax 53409 Hybrid Solutions Ceramic Spray Coating.