I have a really tough time shooting shiny coins and I will share a tip with you I learned a long time ago that helps. There is a very cheap hair spray (I assume it is still around) called AquaNet. I probably bought AquaNet because it was very cheap! Other brands of hairspray may work just as well. Regardless, mist your shiny coin with the hairspray until the surface of the coin turns "flat." Flat, means there is no reflective quality.
Once the coin is photographed then it is a very easy chore to wash the hair spray from the coin's surface with water. I don't think the hairspray would harm the wax on the surface of a waxed coin. The next time you encounter a coin that is giving you a great deal of reflection then please try and let us know how this trick works for you.. God Bless.. Jerry..