The Supreme Court and I seem to be at odds quite a bit. However, the Constitution does not authorize a central bank and it states that only gold and silver may be legal tender. Therefore, a central bank and fiat currency are both unconstitutional.
Well, I'd suggest that where you and the Court are at odds... the Court wins. You can disagree with decisions... you can curse the day the court was created... but nonetheless, is what it is and the Court is the final arbiter of constitutionality (something I had to swallow after Bush v Gore).
Congress is given the power to "coin money". I'd think that means paper, too. The Constitution has never been as literally interpreted as you might wish. And Congress always has the right to regulate commerce and do what is "necessary and proper".
I think you'd lose on this one too.