This article about the https://en.wikipedia.org/wiki/United_States_dollar#History shows that some of the colonies had their own currencies. It seems from the article that the dollar was around concurrently with the other colony's currencies. At what point in time did all of the colonies or states stop making their own money and use the dollar?
The Congress shall have power ...
To coin money, regulate the value thereof, and of foreign coin ....
No state shall ...; coin money; emit bills of credit; make anything but gold and silver coin a tender in payment of debts, ....
So as of the U.S. Constitution coming into force only the Federal Government had the authority to coin money or emit bills of credit, or to create a legal tender other than gold or silver coin.
The similar authority under the Articles of Confederation was much weaker, requiring only that all coin struck by the individual States adhere to quality standards set by the Congress assembled in order to ensure a uniform coinage across the nation:
Section 4. The United States, in Congress Assembled, shall have the sole and exclusive right and power of regulating the alloy and value of coin struck by their own authority, or by that of the respective States; ....
As regards individual States: The Historical Account of Massachusetts Currency (1839) notes that on Nov. 17, 1788 (page 207, top):
Aware that, in compliance with the National Constitution, the right for the States to coin money had ceased, [Commonwealth of Massachusetts] Assembly order that the copper on hand for the making of coins be manufactured as soon as possible, and then for all the workmen to be discharged.
And again on Feb. 25, 1795 (pp 211):
As confirmation of what Congress had previously done, [Commonwealth of Massachusetts] Legislature enact, that from the first of September, 1795, dollars, cents and mills [i.e. the currency of the United States of America] shall be the money of account in Massachusetts.
For several decades following this private banks, as authorized and directed by the various States, were allowed to issue bank notes, denominated in dollars and convertible to U.S. specie. To this end the Massachussets Legislature again enacted, March 4, 1809:
For the purpose of uniformity in our bank bills as well as to prevent counterfeiting them, they are required to be struck from the stereotype plate prepared by Jacob Perkins.
Though printed under State authority these are not in any sense a public currency of the several States - as they are guaranteed only by the issuing bank and not by any government authority. As such they were not legal tender, and traded at a discount relative to official specie coined under authority of the national Congress. As of Nov. 11, 1809, discount rates on various bank notes, by bank, were listed (relative to Boston bills) at
Lincoln and Kennebeck Bank bills at 3 per cent., Hallowell and Augusta at 2 to 3, Penebscot at 12 1/2, and Northampton 12. The discount rate on various bank notes out of the State [termed foreign bills] were greater than what is just stated.