Have you tried plain white paper?
If you're expecting perfectly white backgrounds from-the-shot you're bound to be disappointed. The reason is that your camera's focus
area, if used correctly, will be measuring the light levels within the bounds of the coin to determine the proper exposure. On a dark copper coin this may mean that you do get the background so whitewashed that it appears perfectly white like you intended but on a lighter coin the shutter must remain open for less time - giving, of course, less time for the camera to "develop" the background into a featureless white
area!
Knocking out the background in photoshop, or pretty much any other program, is very easy. You just use the tool that selects
area by light level (magic wand in PS) and click around until all but the coin is selected then delete it.