[The Congress shall have Power . . . ] To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures; . . .
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
Which part gives them power to ban alternative currencies?
This?
No state has to recognize an unconstitutional currency.