Mark,
The best way I have found to remove those type of caps (the ones that cover just the hub and not the lugs) is to pull the
wheel off and take the back end (handle) of a screwdriver and give it a decent whack from the inside of the
wheel, almost like you are stabbing the back of the center cap with the handle of the screwdriver. If you have an old leaf-spring bushing or something similar, you may be able to stick that into the back side of the center cap and hit that with a mallet to pop out the cap. Make sure you either catch the cap or put something soft for it to land on so you don't scratch it up.
Hope that helps. I have never done this with the actual Genesis caps, but it has worked well on several other wheels (MK3 Supra, Volvo wagon, etc...).