Well, there is actually ample historical precedence for how this would be accomplished. When credit cards first achieved widespread usage in America, there were no stores accepting them. The credit card was invented before there were signs in every window proclaiming “We accept all major credit cards.” How was this possible? How could a private means of exchange become liquid?
By the provider of that means of exchange offering certain benefits to merchants willing to accept it. In this case, credit card companies offer guaranteed payment on debt, and simplified transactions. They even offer the less obvious benefit of encouraging customers to spend more money than they may otherwise by divorcing the expense from the point of sale. Because of the money illusion, customers are more willing to swipe their card for one hundred dollars, and send a hundred dollar check to the bank later, than they are to remove five twenty dollar bills from their wallet for the same purchase.
These may not seem like incredible benefits to you, but look around. What major company doesn't accept credit cards these days. By offering a few simple and inexpensive benefits to merchants, credit card companies have convinced nearly everyone to accept their private means of exchange, and even to pay a fee to do so.
Private currencies could do the same. They could offer benefits to merchants such as, guaranteed exchange in any currency of the merchants choice for their currency, or even offering to discount their currency to merchants who agree to accept it by 1%. While that may not seem like much, imagine what a business could do with a 1% increase in operating funds over the course of a year. The company providing the currency would make the expense back when everyone decided to buy and use their currency because of the vast number of merchants willing to accept it.
Merchants either accepting or requiring a variety of different currencies wouldn't be a major burden on the consumer either. Consider that regardless of your individual bank, all companies that accept checks will accept your check. This isn't because they know your bank and have an agreement with them specifically. It's because banks have agreements with each other to honor debts and credits. This is done through clearing houses who oversee the financial transactions. This system would continue to exist.
And if you used automatic deposit and withdrawal from your bank account? Banks that wanted your business would offer services where they would convert your currency to the currencies accepted by your creditors at the most favorable exchange rate to you. Any bank that didn't offer this service would run the risk of losing their customers to one that did.
So liquidity isn't really an issue either. Private local currencies, such as the Ithaca Hour, have no problem encouraging local companies to accept them as means of exchange. In fact, companies are happy to do so, because it increases their business and frees up other forms of currency for trade outside the community.
What other concerns do people have, now that we've addressed fungibility, liquidity, and stability? Well, what if the company providing the currency goes bankrupt? Would that leave the bearers of their currency penniless?
Any reputable private currency company would make their business and management practices open to the public and highly transparent. Any company that didn't would automatically be viewed with skepticism and avoided by most customers. In fact, some private currency companies already do this and as a result, the well managed companies are able to increase market share and stability. If consumers saw their currency provider struggling, they would have an incentive, and more importantly an opportunity, to take their business elsewhere. An opportunity you don't have under the current fiat money system.
Additionally, competitors who recognized a failing currency provider could offer incentives to his customers to move over to their currency, such as offering to exchange his currency for his competitors at 105% value. Customers would be only to happy to switch over to his currency for a 5% increase in their holdings. Again, this already happens between banks who offer financial incentives to their customers to close their checking accounts with their competitors and open new accounts with them. These aren't ground breaking concepts, their already in practice.
In reality, private currencies already exist in the form of private credit cards, checking accounts, local currencies, and electronic money transmitters. These are real private means of exchange, they just aren't generally thought of in those terms. They aren't a fairy tale or a myth, and the systems for their viability are already in place. The only real difference is that most of them are backed by fiat money instead of real commodities, and that change would only be for the better.
Governments don't want private currencies because in order to be viable they would have to be stable and resist inflation, and that doesn't allow for them to steal the wealth and leave the people empty handed. So they want you to be scared. Hopefully now you're less scared and more equipped to consider the idea of private currencies and stateless economies. Hopefully you can now take a rational view of how they would work, and what you stand to gain. Hopefully now you have begun to think about what you want in a currency, and who's offering to fill your market demand. Once we educate the uneducated, only the truly evil will stand in the way of rational thought.
That will be the easy part.