My son has been really into coins for a while and I decided, after suggesting to @zackboston a use for a Structure Sensor 3D scanner, to make my own coins for me and my son. It turns out the process of designing a good looking coin was a little more difficult than I expected. Our coins might not feature what your coins would: for instance, we have no year stamped on them, nor the denomination. However, my son assures me they are valuable. My son asked if we could put some type of phrase on them but I pointed out that the resolution of the Makerbot Replicator that we use around the house probably would not render the tiny words too well.
I started with a Thingiverse thing that contained a number of different play coins and used Tinkercad's hole shape to mask all but this coin. At first we played around with a new 3D scan of my son wearing a laurel headband, like a Roman emperor. This design lost too much detail in the 3D scan and ended up with too tall a profile.
I ended up using a scan of my son from last year as well as one of myself from last year, too. I masked everything but our heads, then bisected the head with the hole shape.
The halved head was reduced to 2 millimeters tall and applied to the obverse side of the coin.
The coin had a star on the obverse and reverse sides. Originally I played around with reducing the depth of the star but keeping it.
However, after getting the heads dialed in so well I decided to customize the reverse side as well.
I added a cylinder shape the depth of the reverse side to fill in the star. Additionally, I isolated part of an Artemis Papert TurtleArt design and turned it into a hole that is etched into the reverse side cylinder only .25 millimeters deep. This was our anti-counterfeiting measure: each coin contains a different part of the design.
The coin with my son's visage is larger, at 40 millimeters diameter, while mine is 35 millimeters and my wife's is 37 millimeters.
Creating your own coins would be a great project involving design, 3D scanning, 3D modeling, math, art, programming, and 3D printing or even milling if you have a CNC. Furthermore, a class discussion about the symbolism inherent in money and coins could generate many ideas about what and who should be on a coin.
I am carrying a couple of the coins in my pant pocket to tumble them with my wallet, leatherman, and each other and give them a good patina. Currently they are printed in a day-glo yellow filament, but I think a silver or gold filament would look great, too.