There are ways to build something like this to:
1) Audit the production process so keys can't be stored, if you trust the code (and the hardware)
2) Stuff coming from the production process goes into tamper-responding smartcards which can prove they are real devices and untampered (preventing counterfeiting and double spending)
At that point, as long as you trust the cryptography and tamper-resistance (of mint hardware and coin hardware), you can trust that a coin someone hands you is valid.
It's probably about $5-10 to make a "coin" with these properties, and $200-300k to make a mint. There are a lot of hybrid online/offline token based currencies which would meet the requirements, but assuming the right hardware, you can build the whole thing as a wrapper around arbitrary data.
At that point, as long as you trust the cryptography and tamper-resistance (of mint hardware and coin hardware), you can trust that a coin someone hands you is valid.
It's probably about $5-10 to make a "coin" with these properties, and $200-300k to make a mint. There are a lot of hybrid online/offline token based currencies which would meet the requirements, but assuming the right hardware, you can build the whole thing as a wrapper around arbitrary data.
There is still no real market for this, though.