Dupli-Color matte black auto body touch-up paint is a perfect match for the Polycoat black. But almost any autobody matte black touch-up paint is, too. Sometimes, with small chips, you simply can't tell. For big chips, the stuff in the small bottle, because it's thicker, will fill up a gap a bit better. You might even be able to mask the gun up and spray paint some of the frame wear pretty well using the spray can. Very light coats applied with a light hand. You may have to repeat in a few months -- but it's not expensive or hard to do.
I've found that for minor scratches, you do better with the larger spray cans of the same paint. Spray a little on a piece of aluminum foil or into a plastic cup, and use a model paint brush to apply it. The Spray paint is a bit thinner than the little touch-up paint bottles of paint and will look better if you're careful in your use of it.
Birchwood Casey has never been that good, in my experience. The auto body paint does better, but nothing short of refinishing (which will eventually leave you where you are) won't be a perfect repair -- but will look much better.