I dunno, why not? You can have one right now. You will be required to use one (1) US dollar in the transaction in order to qualify for protection from the courts, but given the predations of the Federal reserve, this seems a minimal expense. Otherwise, go ahead and denominate your deals in anything you like: ounces of gold, bushels of wheat, ingots of tin, barrels of oil, or anything else you can dream up. You will have to convert back to US currency in order to pay your taxes, but I doubt Ron Paul's system would let you pay your taxes in dried codfish either.
Nor are you limited to barter. You can simplify things by obtaining a certificate which entitles you to some quantity of gold or other commodity--right down there at your local metals exchange. One can buy a bunch of gold and melt it down to coins of a fixed weight of gold. They won't be legal for paying your taxes, so you'd bear some currency risk when tax time rolled around. But you would under any system with multiple commodity-backed currencies, because their relative supplies and demands would fluctuate.
So why haven't you done this? If you say, because no one would spend it, you've hit on the reason for government money; it massively reduces transaction costs to have a single accepted currency.
One common response is that "bad" government money is driving "good" private money out of the market. But that assumes what you want to prove. If government money were so bad, people would turn to substitutes; if you go to any country where the government massively inflates the currency, you'll notice that people turn to dollars or gold in preference. Note that people who could choose any money they want turn to the dollar as their store of value. This is less true than it used to be, for reasons that have very little to do with our central bank's policy, and much to do with global capital flows. But it is still very true. Which is why I say that the gold standard is a solution in search of a problem.