Any non-abrasive polish will work well so it doesn't strip the finish of your table.
You can try nail polish remover or paint remover.
A wax based polish.
If the black table is made of a black wood like ebony then finger nail polish remover should work fine. If the black table is painted, it is a little trickier. Hardware stores sell blades for paint scrapers. They are called single blades. They have a blade on one side and a small piece of metal on the other for the paint scraper. You can lay one almost flat with the blade just touching the top of the table and slowly scrape off the nail polish. If you get the angle too high, you will gouge the table. Start off slowly.
try spraying a little WD40 on it. this usually works better than finger nail polish remover or anything with acetone in it, and doesnt strip the paint. Lemon furniture polish worked really well for me. :)
Poop help nail polish get off.
Nail polish remover... or scratch it off... It does eventually fall off.
Rub it with Goo Gone or nail polish remover, then soap and water.
You can remove nail varnish remover and cotton wool that stuck to the remover from a wooden table using a Q-tip and nail polish remover. Slightly moisten the Q-tip with the nail polish remover and carefully dab the pieces of cotton wool that are stuck to the table. They should come off quite easily.
To get nail polish off camera case, use thinner (acetone) or nail polish remover.
nail polish remover
Fingernail polish remover. :-)