I believe that the US Constitution reserves the right to "coin money" to the federal government alone. They did not want 13 individual states continuing to print their own money or the hassles of trying to figure out exactly what each state's money was really worth in relation to the money of other states.
As to the states... there is nothing whatever preventing them from minting scenic state "medallions" from copper or brass, silver, and gold in 1/10, 1/4, 1/2, and 1 oz. sizes. If their residents choose to use these, uh, commerative pieces, as money, well, no one would be stopping them. Note that none of these medallions would have any dollar value on them, just the values for metal, weight, and purity.
Prices for goods and services could be listed in metals and weights instead of dollars. "Want a 100 lb. bag of grain, sir? That'll be 1.75 ounces of silver"... or whatever would be fair in that market.
In the case of Utah and their recent law about gold and silver
US coins being used as money - I bet that a lot of that was so that PM coins could be exchanged without anyone having to pay a sales tax on them or a tax on any profits that resulted. After all, if a gold coin is actually money, there would be no tax on exchanging it for a wad of paper bills or for other coins, right? We do not pay a sales tax now for exchanging one form of money for another... trade two $10 bills for a $20 bill and there is no tax owed.