Hi, ceaton. What camera are you using? Does it have a macro feature? I've used both a "point and shoot" type camera (Canon S3 IS) and a digital SLR type with a macro lens. The latter type costs more, but is easier to use. However, the P&S cameras, if they have a macro feature, can take some outstanding coin photos. It all comes down to light.
"Macro" mode is typically indicated by a little "flower" symbol on the screen or in the viewfinder. On the S3 IS there's a button with the flower symbol that you have to push and hold for a couple of seconds to set the macro feature. I'm sure nearly all $500 cameras have macro, but it sounds to me as though you maybe aren't using it?
If you are using the macro feature, but still have to focus from such a distance that the coin is small in the viewfinder, you must be sure to use the largest photo size your camera allows, so you can crop the picture and increase the size of the coin after taking the picture.
Just some thoughts...Also...if you post a picture or two, we can look at your results and maybe give some more definitive advice.
Keep shooting!