Probably a high heat durability paint found in auto parts stores, and walmart type stores may carry it. They have quite a bit of choices in color and glosses or flat .

The Eastwood paint has a satin finish. Here is the product description.

Chassis Black® Satin Paint Qt

Not glossy, not dull, just right! Authentic 60-70% gloss looks great on suspension parts and frame. Available in Qts. (covers 40 sq. ft.) and Aerosol (covers 8 sq. ft.). Proper for all makes and models. Tough formulation resists chips,corrosion and temperatures up to 300 degrees F ; covers fast, up to four times the coverage of similar size Aer.; average car uses just 3 to 5 cans for entire chassis! (Available in quarts,sprayable only) Works great over bare metal, Eastwood Rust Encapsulator, or Eastwood Chassis Black Primer.

I had my swing arm modified a couple of years ago, then bead blasted to bare metal. I used Krylon sray finishes for the primer and the finish. After two coats of primer, and sanding with 600 grti paper, I applied several coats of gloss black. After more than 30k miles there is still no chipping or rust. One cuation about doing the painting your self, you can’t wait too long for the paint to harden. I did this work in the winter and set up a heat lamp to accelerate hardening. It was still more than a week before the paint was truely hard enough to reassemble the swing with out fear of damaging the surface.