I don’t think 2 currencies will work because people will pay their debts in the fiat money and lock up their gold money.
http://en.wikipedia.org/wiki/Gresham’s_Law
Remember that Article I, Section 8 gives Congress the power to coin money...it also prohibits the states from issuing bills of credit (in the parlance of the Founders...that was paper money). Did this mean the feds had the power to issue paper money? Of course not, the feds had the power to coin money...but nowhere was it given the power to emit bills of credit...and, hard as it is to believe now among people who don't know much about the Constitution, it was well understood at one time that any powers not expressly delegated to the federal government in the Constitution, the feds do not have.
Anyone familiar with the debates over ratification of the Constitution will remember that one of the strongest arguments the Federalists had against the Anti-Federalists was that the US Constitution would do away with the scourge of paper fiat money...the tool of free-spending, fiscally irresponsible governments everywhere....and something that was causing financial chaos in most of the colonies
So, economics aside...those who are faithful to the Constitution can only advocate a gold-backed dollar (or some other precious metal-backed currency)...either that, or advocate an actual amendment to the Constitution to give the federal government the power to issue fiat currency