How to polish Wilson Audio speaker

+1 for Lak's comment.
B

Here's what an account service manager from Wilson Audio had to say: 
Hi, Yes we use an automotive paint process, base coat/ clear coat. Anything safe to use on an automobile is safe to use on our speakers…
As you may surmise, there are some excellent detailing products out there for cars. Pick your favorite….I would be cautious with a powered polisher unless you know what you are doing, you may burn through the clear and base coat…
We use the 3m micro fiber cloth rags….I would use a rag that you’ve known to work well with automobiles as well.
Best Regards,

Plexus Plastic Cleaner or Meguiars Ultimate Polish works best, do 3 times a year and periodic microfiber cloth dusting.   If you have micro hairline scratches or hologram scratches it involves cutting, buffing and polishing by machine but be careful you don't want to burn through the clear coat.  Sophia 3 are amazing aren't they?  They seem to sound better scratch free ;-)

On all of the Wilson Audio Speakers that I have owned, including my current Ferrari Sebring Blue Sasha 2s, I've used Meguiar's Ultimate Polish & Ultimate Quik Detailer (when dusting), with Meguiar's Supreme Shine Microfiber Towel and it works great, leaves a deep-color high-gloss shine - highly recommended.

Wizards Shine Master.  A breathable polish and sealer that effortlessly wipes on and off, smells like cherries, shines like a mirror, and lasts years on my garaged motorcycles.  Plexus is good.  This stuff blows it away.

jmvs has offered the best solution. When buying used speakers, if the speakers were not cleaned properly (not using micro-fiber cloth to dust or clean) swirl marks may be present. To remove these, I have used Meguiar's Swirl Remover with light application, followed up with Meguiar's Ultimate Polish. The Quik Detailer is great in between waxing....just like your car.