The authority to coin money is specifically granted to Congress by the U.S. Constitution. Article I, Section 8 states that Congress has the power "to coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures." This clause establishes Congress as the sole entity with the power to create and regulate currency.
While the Federal Reserve plays a crucial role in managing monetary policy and regulating the supply of money in the economy, it does not have the power to directly coin money. The Federal Reserve issues Federal Reserve notes (the paper currency commonly used) but this issuance is derived from the authority granted to Congress. The President does not have the power to coin money either; instead, the President appoints members to the Federal Reserve Board, which oversees the Federal Reserve. Finally, state legislatures are explicitly prohibited from coining money or issuing their own currency, which further solidifies Congress's unique authority in this matter. Thus, the correct answer is Congress.