Best way to clean glossy finish on speakers?

@macg19 @mijostyn is 100% dead on, though I didn't see him mention that not all foam is alike. An inexpensive rotary buffer with a soft foam pad and Menzerna 3500 or a similar fine polish will remove swirls, and return you to a brilliant shine That said though, extreme caution around the drivers, or even hand polishing if you are having difficulty controlling the buffer is a good idea. Some are base/clear coating these days, which is a HARD finish comparatively, and most are probably still using lacquer, both have been used for automotive finishes, though clear lacquer hasn't it has identical qualities otherwise to lacquer paint. Therefore automotive polish is fine. Using things like ceramic or graphene coatings can be problematic as the better ones leave your finish unbelievable slick. IOW, easily dropped. Build up  of product can be an issue as well. If I was unsure whether the finish was a softer lacquer or a harder clear coat, I'd avoid using something that might be difficult, meaning more Menzerna 3500, to remove, but that's just me. A wax or coating should add brilliance, but the Menzerna 3500 may meet all your goals.

Interesting comment about cleaning drivers cones above.

Never thought to clean them, exactly how does one go about doing that? Maybe a light dusting from a swiffer?

Because people are around and so forth I keep the covers on and they look fine.

Sprayway Ammonia free window cleaner and a clean microfiber towel all day long!

@vandy357 

You asked about a ceramic product and I told you. After rubbing out with a fine polishing compound like Menzerna 3500 all you need to do is wipe off occasionally with a fast evaporating product one would normally use for cleaning windows but without the blue dye. I use 50% isopropyl alcohol in distilled water and a cotton or microfiber cloth. You could also use a quick detailer. Most clear coat finishes on modern loudspeakers are going to be polyester which is extremely tough, tougher than acrylic lacquer. 

I use Chemical Guys microfiber towels (yellow) on my Wilson Sabrina. I only remove dust. These towers are super soft.
I don’t use sprays or water. if I move my speakers I wear white cotton gloves to avoid fingerprints. When I had a Rega gloss black turntable I used the same towels with Meguiars Ultimate Quick Wax. Worked great. I haven’t had the need to use the spray wax with the speakers.

These are the towels. These are also the only towels I use on my car’s metallic black paint.