Since the feds abandoned circulating gold and silver coin, the states must create a gold or silver backed currency system under the U.S. Constitution, which says states cannot accept anything except gold or silver coins for repayment of debts. That excludes the worthless cupronickel and fiat paper money the Federal Reserve churns out daily.
Unfortunately, that's not quite what the Constitution says.
Article I, sec. 8, cl. 5, gives Congress the power to coin money:
To coin money, regulate the value thereof, and of foreign coin, and fix the standard of weights and measures;
and Article I, sec. 10, cl. 1, merely prohibits the states from making anything other than gold and silver legal tender in payment of debts:
No state shall enter into any treaty, alliance, or confederation; grant letters of marque and reprisal; coin money; emit bills of credit; make anything but gold and silver coin a tender in payment of debts; pass any bill of attainder, ex post facto law, or law impairing the obligation of contracts, or grant any title of nobility.
Put that together and the result is that Congress can make money and the states cannot force any creditor to accept anything but gold or silver coin as satisfaction of the creditor's debt.
The prohibition on states - by legislation or court case law - from making anything but gold and silver legal tender was intended to deal with the pre-Constitution problem of states creating scrip - the true forerunner of fiat money - that it would issue to people, frequently as advances against their crops (the problem cropped up - pun intended - mostly in the smaller agricultural states) and which the states would frequently make "legal tender," meaning that a farmer who had scrip from his state government could satisfy a debt he owed by tendering that scrip to his creditors. That might have been acceptable if each state had a closed economy because that creditor could then use the scrip to buy something in turn from someone else. Unfortunately, the states weren't each closed economies and so serious problems arose when a debtor would attempt to pay an out-of-state creditor with his in-state scrip, which of course was nothing more than pretty wallpaper outside of the debtor's state.
The issue also made the requisitions system of the confederacy, under which the Continental Congress could only raise revenue by requisitioning revenue from the states - meaning that it was essentially asking each state to tax its own citizens to raise that revenue. In states where hard currency was scarce, the taxes would be paid in that state's scrip which was, of course, worthless outside that state, and particularly when trying to pay the debts the Continental Congress owed to foreign lenders, particularly the Dutch, which were incurred to pay for the American Revolution.
The prohibition against making anything but gold or silver legal tender goes hand in hand with the prohibition on states passing any law impairing the obligation of contract, which basically prohibits a state from freeing someone from the consequences of what was a legally binding contract when it was made - in other words, no state could enact anything that in substance discharged a person's debts. This was also a big problem in states that were short on hard currency because they would sometimes invalidate originally legal, binding contracts under which in-state residents owed debts to out-of-staters, by, for example, making it impossible for an out-of-stater to enforce the contract in in-state courts.
Since Congress' power to coin money is not limited to coining gold or silver, Congress can create paper fiat money and can make that fiat money legal tender in the individual states.