If you want to cast anything in precious metals, your best bet would be to do lost wax/investment casting.
However, their is several pieces of equipment as well as materials you would need to accomplish this.
Here are a few links about lost wax casting:
http://www.instructables.com/id/Lost-Wax-Casting/
http://www.ganoksin.com/borisat/directory/library/subject/33
I would suggest that you either have the casting done by a company that will custom cast what you intend to replicate or have made, or find a community college or artistic group such as a maker space, etc, take the class or classes required and do it in class using their equipment and consumable supplies. You can easily learn how to cast in one semester.
There is another easier option for making a coin that does not involve casting, you can use precious metal clay or PMC by it's retail name. This is a metal clay that uses organic binders. Because the binders are organic, once fired the organics are burned off and you are left with a pure metal result. PMC can be purchased in several different alloys. It does shrink a bit after you design what it is you are intending to make, but this might be an easier option to accomplish what it is you are attempting.
You might choose a company such as this to do the casting for your design:
http://www.milwaukeeprec.com/lost-wax-casting.html
You might even find a art group, or again a makers space or otherwise where you can learn how to shape the clay, and then use their equipment to fire it. Here are some links on precious metal clay:
http://www.riogrande.com/category/metal-clay,-glass,-enamels-and-resins/Metal-Clay
https://www.etsy.com/market/precious_metal_clay
I actually make precious metal clay myself, but I'm not ready to market anything yet as I'm still working out ways of preventing shrinkage. I wouldn't attempt making the clay yourself but instead purchase what you need from Rio Grande in the provided link above or from some other reputable retailer. I believe Rio Grande still purchases metal clay scrap, so you can also sell your excess clay back to them.
Hope this helps.
Scott