I'd look into finding a dentist type rotary tool... something with high precision and high RPM. The thing about dremels is that they're really not made to be able to be run for hours on end. So even if they were very accurate and vibration free (which they're not), they wouldn't be suitable.
Hopefully someone else will shed some light on this topic. I've never done any coin engraving myself, but I've seen it done at trade shows using lasers and EDMs. I'm curious as to whether a rotary tool is capable of the same surface finish without a lot of post machining cleanup work.