If you're trying to take pics of the whole coin, why do you need a microscope? What I'd recommend is to simply install a reversed lens onto the front of the existing lens. Problem is your camera's lens doesn't seem to have any provisions to mount anything on it. Given this, I'd recommend to buy a 50mm EL-Nikkor and hold it up to the lens while the camera is on and lens extended. You could tape it to the camera for use when it's on and un-tape it before you turn the camera off. Since your lens is a 4.4mm to 66mm zoom, your magnification range would be:
4.4/50 to 66/50 or 0.1x to about 1.3x
Dollars need about 0.2x on your camera, and Cents about 0.4x, so this should give you a full range of magnification where you can image the whole coin. Plus at full magnification you can zoom in nicely to view small details. Working distance at maximum magnification will be around 2 inches, far enough to get lights in fairly easily.
You should be able to pick up a 50mm f4 EL-Nikkor for $20-$30 on
ebay.
Ray
PS>>>You may get a bit too much vignetting with your f3.5 aperture, so I am not 100% sure you can image an entire Dollar as the vignetting may cut off the periphery. I tried it on an old Coolpix with 5.8mm f2.8 lens and the vignetting just cuts off the outer edge. Works OK for Halves and smaller. Your lens is completely different from mine so it may work fine, but this is a risk you take with this approach