What are the parts used for? What is the environment, service, handling, exposure to sun, snow, chemicals, etc.?
Black oxide provides essentially no corrosion protection.
Paint (with proper surface preparation and primer) can be pretty good corrosion protection. Unless it gets scratched or chipped down to the base metal, then it's useless.
Powdercoat is the same, except that it is harder to scratch or chip.
Paint and powdercoat will both add thickness to the finished part, so if things are designed for a tight fit you'll need to take that into consideration.
You could also do a zinc coating with a black chromate. There are probably some other coatings that are black.
Is aluminum an option for the base metal? That would open the options to include a black colored anodize.