High value coin clipping would become more common
Ancient and medieval society was primarily based on the bullion system where the value of a coin came primarily from the weight and types of metals used, and the actual coins themselves were not that important. This was especially true when trading between cultures. This means that when you have a coin that is worth too much, you could clip it (cut it into smaller pieces) and the pieces would still be considered legal currency.
Depending on when and where you are talking about, a fair day's worth of labor was normally considered worth about 80-240 grams of copper, 4-12 grams of silver, and 0.2-0.6 grams of gold with the average coin weight being around 8 grams. This is all of course a huge oversimplification since we are talking about hundreds of societies across centuries of economic variation, but these seem to be about the averages in Europe throughout history.
As often as pop culture makes references to "gold" in terms of historical currencies, gold was not commonly used in day-to-day life in the medieval world because it was worth too much. A single gold coin could represent your entire month's income for a typical lower-middle class freeman. Instead gold was mostly only really used when making very big state level transactions.
Now in the case of your fairies, these smaller coin pieces would be far more convenient than full sized coins; so, instead of being paid with a stack of copper or silver coins at the end of the week, they would more likely accept a single piece of clipped gold coin. These clipped gold coins could then be traded back to the humans for what the fairies would perceive as bulk transactions, or they could be further broken down and re-minted by the fairies to make even smaller coins that make more since for use in their own community. Tiny little beads of gold could be worth just as much as a human sized copper coin; so, by trading primarily in gold the fairies could carry just as much value of coinage on their person as the typical human would carry in silver and copper.
Based on all of this, when dealing with historical fantasy settings I prefer to keep things simple with the 1/20th : 1 : 20 rule where by a copper coin represents 1/20th of a day wage, a silver coin is a day wage, and a gold coin is 20 days wages unless you plan to use a specific coinage system from a specific place and era. Since "day wages" were normally based on the pay given to a common soldier, and the average US common soldier makes 12.50 USD/hr, this means we can estimate the average value of historical European bullion coins to be approximately:
- Copper = \$5
- Silver = \$100
- Gold = \$2000
So, even if your fantasy setting says that a fairy's coin pouch is only big enough for 1-2 coins, you can see that using a gold standard would still allow them to carry quite a bit of money on their person.
The biggest hurdle will be trust
The fairies can use innate magic for flight and simple illusions and not much else
A species that can naturally cast illusions makes the use of currency (and commerce in general) much harder. Sure, it is easy for a human to give a fairy a gold sliver in payment for a service, but what happens when a fairy tries to pay a human in gold? Is the fairy really giving you gold or is is a piece of lead that has been illusioned to look like gold?
Your human merchants will need a simple and reliable method for dispelling fairy illusions or else the lack of trust will eventually cause the humans to ostracized or even drive off the fairies from their town.