The original (thick) coating appears to be a plastic, which was probably intended to attenuate valve train noise. With heat/time it tends to bubble and lift and look ugly.
Aluminum requires some special preparation to ensure adhesion of a paint finish. The first step is to chemically strip the paint or other coating and then mechanically clean the surface with a soft media (bead blasting) so as not to unduly change the surface texture.
Go to an automotive finish supply store and buy a bottle of "Alumiprep" and "Alodine". Alumiprep is a mild phosphoric acid solution that etches the surface of aluminum to remove oxidation. Follow this up shortly with the Alodine, which reacts with the surface to from a chromate compound to prevent oxidation. Follow the directions on the bottles for dilution and dwell time. Immediately after drying the part following the final water rinse to wash off the Alodine, paint the cover with a flat or semigloss engine enamel.
If you're not sure if you want flat or semi-gloss, buy both and start with the flat. If you want more sheen, just consider the flat to be a "primer" and top coat it with the semi-gloss. I prefer the flat and then coat it with a 50/50 mix of Armor-all and distilled water from a spray bottle and work it in with an old natural bristle paint brush.
The Alumiprep/Alodine process is what is used to prepare aerospace aluminum structures for painting.