According to federal law, you are not allowed to fraudulently deface or mutilate any U.S. or foreign currency in use in the United States. However, "fraudulently" is the operative word. Essentially, if you never try to use the coin as currency again, then drilling a hole into, or otherwise mutilating, a coin is not illegal. Otherwise, operators of the popular coin press machines would be in serious trouble. However, if you try to pass the coin back into circulation, then you are committing a serious crime.
Clamp the coin on a small block of scrap wood.
Align the tip of the centre punch to where the hole should be. Tap the back of the centre punch with the hammer to create a small indention, which will guide the drill bit.
Attach a 1/16-inch drill bit to your drill, as instructed in the drill's manual. You can use larger bits if you need the hole larger than 1/16 inch, but for very large holes, it's better to start small and widen the hole by drilling with incrementally larger bits.
Select a slow speed on your drill, according to its instructions. This usually involves simply sliding a selector switch.
Place a small drop of lubricating oil on the indentation left by the centre punch. This will reduce friction and heat, which protects your drill bit.
Place the tip of the drill bit into the indentation and apply downward pressure with the drill running. You should be able to feel it when the drill breaks through the opposite side. Run the drill a few more seconds to smooth out the inside of the hole, then withdraw the drill.
Replace the bit with a larger one, if you need a larger hole, and repeat the drilling process. The smaller hole acts as a guide and allows the larger bit to bite into the metal. You can repeat this process until you have the right-size hole.