The coin is made of nickel-brass, with brass being copper and zinc. I assume it's the copper that caused the spots.
Try putting it in a bath of acetone for about one hour, make sure that the green spots are in direct contact with the acetone. Then clean off the coin using distilled water. Pat it dry (don't rub).
Alternatively, try putting it in a bath of distilled water with some baking soda dissolved in it for about one hour. Then clean with distilled water and pat it dry (don't rub).
I hope this helps!