As said in comment above, this could be done with texture displacement, like this:
of course the provided texture is probably not trimmed enough but you get the idea.
Note: I used a default circle, then filled with about 500 vertices, then subsurfed 5 times... which brings you about 1000x vertices, otherwise your coin face will be much more rough than this... of course it's damn slow.
Another way could be to vectorize the b/w image to svg (eg: use inkscape), then import svg into blender and then extrude... then add a cylinder "body", refine, and try exporting to .stl and similar.
eg., it could end like this
Note:the vertices count could be somewhat smaller in this case, but as usual, the more detail, the best results. In this case you can't easily smooth using subsrf, though... you could need a lot of mesh adjustment to correct (very) bad topology.
You have to find the best settings, it also depends on 3d printer resolution, of course...