Get yourself a forstner bit.
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Measure your coin. If you can't get a bit the same size, get one slightly smaller.
Measure the depth of the coin
Put some tape around the forstner bit, marking the required depth.
Drill your hole, ensuring you keep you drill square.( a bench mounted drill press is best)
Trace around the coin with a nice sharp blade, do it in multiple light passes, don't try and do it in one cut.
Cut down to the depth of the coin, then carefully relieve the hole with a chisel.
Attach the coin with some aryldite or industrial adhesive.
Go slowly , go carefully.
If you're lucky you'll find a forstner bit the perfect size.
Good luck