It sounds like these speakers have a base coat/clear coat system applied. To refinish ,ideally you would wet sand the clear coat with 400 wet/dry sand paper. A block of wood with some paper towel wrapped with the sand paper and wetted with a spray bottle works best so you don't sand unevenly. Once sanded you can spray a your favorite color, do this in multiple coats so you don't get runs waiting at least 15 minutes between coats depending on temperature. After the final coat of paint you can spray on a light coat of clear letting it set up a bit then apply a second heavier coat. At this point it should be left to dry. Next lightly sand the clear and apply another coat of clear. To achieve that super glossy finish color sanding and polishing will need to be done. Depending on requirements and skill level you may not need to/ want to do the color sanding which is optional. Duplicolor is my product of choice if I spray out of cans. Since I have a compressor and hvlp spray guns I use Nason automotive for my large projects. I suggest a practice run before doing the project.

Richard