LOL, Red, so are me.
The US managed to become the world's biggest economic power before the Fed was put into law in 1913, so obviously it's unnecessary to have a central bank for the country's well-being.
Let's begin with what the Constitution says on the subject of money.
Article I, Section 8, which lays out the powers of Congress, says "The Congress shall have Power . . To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures; [and] To provide for the Punishment of counterfeiting the Securities and current Coin of the United States . ."
Then over in Section 10 are limitations on what States may do: "No State shall enter into any Treaty, Alliance, or Confederation; grant Letters of Marque and Reprisal; coin Money; emit Bills of Credit; make any Thing 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."
The way I read it, the Fedgov has the sole government responsibility for coining money, which would by necessity be coin of gold and silver if the States are required to accept them. "Regulating the value thereof" simply means establishing a conversion rate, which, IMHO, is a market function that could as well be delegated, and in fact works better that way.
The Founding Fathers had recent, disastrous experience with funny money issued after the Revolution and were very skeptical of letting States print currency. "Not worth a Continental" was an 18-century forecast of things to come: not worth a mark, not worth an old ruble, not worth a peso.
All of these currencies collapsed due to not having something of value to back them and the temptation of central bankers to print money to shore up a sagging economy. The really neat thing about inflation, as you know, is that favored interests (banks, the government itself) who get the money right after it's printed can spend it before prices go up, as they inevitably will. Everyone else has to wait until payday or later, when it becomes general knowledge that more money is in circulation and if you want to maintain your purchasing power you'll want to charge more for your goods and labor.
So what is the solution if we don't have a Federal Reserve?
You go back to a metallic currency standard, probably gold, and you don't print any more paper money in excess of the value of gold in the Treasury.
You don't need actual gold coins, although they're pretty to look at. EFTs and ATMs and all the other modern conveniences would still function as usual. We wouldn't need to redeem our Federal Reserve Notes for gold coins. They could simply be gradually replaced with new notes backed by gold.
My 2c: Why do we have to replace it with anything? All it does is create inflation, much worse than the private banks that it took the place of after it forced them out of business. In the graph linked here , you can almost see the bend at 1913 just getting started and really bending upward about 1945. It started out as a money monopoly and has been such ever since. Why not abolish it, replace it with nothing, and let the government coin money. People will then have gold and silver COIN in their possession. This will in itself create a market for safe places to store money, provide checking services, and lending of surplus funds. Entrepreneurs will open private banks to supply this need. Good banks will succeed. Bad banks will fail taking some depositors' money with them. The world isn't perfect. In living there is risk. If you don't trust the bank, then there are more alternative private places to store your wealth. There is the Treasury. Take your gold and silver coins there and get a gold or silver certificate, which you can spend. See in the graph how we got along fine without a Federal Reserve from 1665 to 1913.