Yeah, you can repaint the coils. I wouldn't lap paint on them thick. Make sure you let it dry good before turning on the refrigerator, even though I'm guessing you don't have it on anyway. Turning it on early could cause condensation, which could ruin your paint job.
I wouldn't put any paint on the burner tube assembly, but it's galvanized, so it shoudln't need it.
A little Awesome on that power cord and some steel wool on the copper supply line will clean it up nice too!
2007 T-286SR Cherry/Granola, #6236, original owner, current mileage: 9467.8 (as of 5/26/19)
1997 T-2653 Blue Denim, #5471
1979 12 1/2' MC, Beige & Avocado, #4639
Past Sunlines: '97 T-2653 #5089, '94 T-2251, '86 T-1550, '94 T-2363, '98 T-270SR