It can not. Reuleaux solids must have an odd number of vertices, or they indeed don't work. It would appear that I didn't have my brain fully on this morning.

To apply the principle of Reuleaux geometry to a regular shape with an even number of vertices, you'd make arcs tangent to the point in question, extending in a curve that increases the coin's diameter as the arc gets longer. The arc would come to an end in a point midway to the next point, where it would intersect with that point's arc. You'd have a star-shaped solid where all geometry external to the inscribed circle are tapered triangles. Kind of neat, but it would be tough to put through a vending machine.