Coin photography is hard, especially when all you own is a cheap, crappy point-and-shoot Nikon and a cheap, crappy USB microscope. But I've been playing with a new photo editor tonight so I thought I'd upload my *poor* initial efforts for your amusement/enjoyment. May I present some pieces I acquired in 1994...
I think if you can diffuse the light, you may have something. It has that 'deer in the headlights' shine.
Point and shoot cameras are fickle beasts for coin photos, since you're at the mercy of how the manufacturer defined the focusing range, and therefore your close-up working distance, but you can get good photos. I did a presentation on this at a few shows, including FUN 2011, using point and shoot cameras. If you have an hour and want to watch it, go to this link. Post the model of the camera you're using and I'll see if I can dig up some pointers from the camera's specs.
Thanks for all the thoughtful responses - the images above were all shot with a $20 USB camera bought on eBay. The lighting was inadequate and the results are poor. I did them to pass the time while watching the ball game; I probably should not have even posted. The Nikon on a tripod does a bit better, when I am more careful with the light. It's a rather ancient (and low quality) Nikon Coolpix 4500. Thanks for the link, Messydesk, I will certainly watch it this weekend. I need to set up the proper lighting and take a more serious approach to this photo thing. I used to shoot film and processed it in my own darkroom, so I'm familiar with the theory; I just need to evolve into the digital age.
OK, that is an old camera (2002). According to the manual, however, you should be able to use the telephoto mode with 30cm working distance and macro turned off. The maximum telephoto length is the equivalent of 155 mm on a 35 mm camera. I plugged this into the spreadsheet I used to make one of the slides at the end of the video. The diameters of a dime and a silver dollar at this setting should be 808 and 1720 pixels, respectively, which is pretty good.