Changing a speaker color

Two points to weigh in on IMO:

- Are you talking about a “usual” satin or flat black refinishing or a gloss black refinishing ? I would not try the latter requiring multi-coat applications, sanding, and fine polishing as a DIY project.

- Without prejudice to the above, a bespoke non-OEM new radical refinishing color ; ( and especially in a DIY effort even with your advanced woodworking skills) will kill its successor owner appeal pool , and especially kill its FMV resale value should you wish to ever sell them later,

No matter what color you choose, I would leave the job to a reputable auto body shop. They will cost more, but they'll do a far better job than you could, and as @akg_ca  said, it will be better for your resale value if you decide to sell.

I've never painted speakers, but back in '02 I was working in a composite shop and I brought in some wooden window shutters, sanded off the old finish, shot them with two coats of USAirways blue and then a coat of clear and they are still holding a gloss shine to this day, so I do not see why it could not be done with wooden speaker cabinets.  . 

Are the speaker cabinets actually made of wood?  I've sanded some stuff before that wasn't wood, and some of it does some goofy stuff after the paint comes off.  I have no idea what it will take to get that gloss white to start coming off . . . maybe just start with a small inconspicuous area with some 80 grit (or even 100 grit) and see how it goes before you start sanding a large area.   

If the original paint is in good condition, it does not need to be stripped, only sanded to a matte finish. After removing all sanding dust, the original paint should function perfectly fine as a primer, assuming it had an automotive-grade finish to begin with. 

Remove the drivers and binding post plates prior to any of this of course, and mask off the holes. 

There is no way to achieve a true piano grade finish without a very controlled HVLP spray system/gun. I recommend that be handled by a professional, otherwise you’re likely to end up with runs, orange peel effect, or trapped debris.