Now we're talking, somebody actually painting up some speakers properly! So you've had some good advice so far with people recommending the Finex FX3000 or the Devilbiss Starting Line. Ideal would be a 1.3mm nozzle (not a fan of 1.4s as they put out too much material and don't atomize as nicely as they should). Both options should be had around the $200ish area. Both of those operate best around 27-30psi at the gun. For these, ideal compressor would be 60 gal 5hp to properly keep up. As mentioned previously it is possible to let a smaller compressor pump back up, just not ideal.
Next order of business is your liquid materials. You will definitely want to spray your speakers in a base/clear rather than a single-stage that comes out directly glossy. Think of single stage like whistling, juggling and doing taxes all at the same time. Base/clear makes it to where you can simplify steps of first focusing on coverage and metallic orientation if doing a metallic color. Then later focusing on smooth passes of clearcoat to make it shiny. Plus if you need to wetsand and polish it is a hell of a lot more forgiving for that too. Just curious, what part of the country are you in? Certain states and counties have some tighter voc limitations on their paints so I could walk you through your options if that's the case.
Last piece of advice is that prep is everything. Take way more than enough time to set up your garage space to be a clean room with good low air velocity ventilation. In a pinch, a lot of box fans turned on low can do the trick, two at the back pushing air across the project, and the rest at the garage opening to pull out exhausted fumes. Plastic sheeting taped to the walls to keep the dust down is a huge help as well.

Also discussing prep, make sure to use wax and grease remover to wipe down your project, lint free spunlace towels to do the wiping (one wet and one dry in a wax-on wax-off scenario) and use a tack rag to get any last contaminants off the surface.
And finally, be careful with your safety making sure to wear a cartridge respirator and have some freakin fun. Message me if you have any questions along the way and I'll walk you through the process.
-Lloyd