As other people have pointed out, electrical phenomena are so commonplace it would be irrational for a scholar to ignore what a piece of fur and a glass stick can show you. Proving that electrical phenomena are the result of the mutual attraction or repulsion of tiny, indivisible charged particles is a much harder endeavor; it would probably take more than one experiment to convince the 'anti-electricians' that electrons are real. Furthermore, you might still be skeptical that electrical phenomena are powerful enough to have powered the machines of the past.
Here's how I would do it, given a weekend with a room full of doubters, and a prepared laboratory full of 1700-1800 tech:
1) Two Types of Charges
Using a variety of triboelectric materials (fur and glass rod, plastic and felt, etc.) I would then take turns transferring the charge (by touch) to some suspended metal spheres:
If we take the fur and glass rod as an example, there are three possibilities:
- I touch the fur to both metal spheres independently. In this case the two spheres repel.
- I touch the glass to both metal spheres independently. In this case they still repel.
- I touch the glass to one sphere and the fur to the other. In this case they attract.
From this, and repeating the experiment for different materials, I make the hypothesis there are are only two types of charges, and similar charges repel while opposites attract. Note this says nothing about charges being discrete; I have yet to show that the presence of 'positive' and 'negative' charge isn't fluid-like (i.e. it's a continuous substance with no 'smallest amount').
2) Crooke's Tube
After demonstrating the rubbing of glass on fur or felt and plastic can separate charges, I would demonstrate a machine that takes that process and repeats it continuously:
The Wimhurst machine depicted above is a hand-powered, high-voltage generator. A Van de Graaff generator would also prove sufficient for this purpose. After repeating the same experiments as in part 1), I would then connect the generator to a partially evacuated glass tube with a single metal surface on the inside as shown:
The metal plate, called the cathode, is present in the back of the tube, while the second metal connector is placed elsewhere (the bottom in this case). The cross in this picture is electrically isolated. When the generator is cranked, cathode rays emanate and project a shadow. The presence of the shadow clearly indicates that something is leaving the cathode, traveling in straight lines, and striking the wall of the tube. This helps confirm that when there is indeed a transfer of some sort of electric material during electric phenomena, as opposed to being imbued with an 'electric property'.
As a bonus, placing an electrically charged sphere next to the tube will deflect the cathode rays, confirming their electric nature.
3) Millikan Oil Drop Experiment
Once you have demonstrated that only two charges exist, and that an actual substance is responsible for electricity, the nail in the coffin is of course the oil drop experiment performed by Harvey Fletcher and Robert Millikan in 1906. I think the experiment could have been performed with earlier technology; perhaps in this society the necessary parts could be scavenged instead of manufactured. Here is a diagram of the experiment:
This is a statistical experiment: as oil droplets enter into the chamber, they receive a small net electric charge. By varying the charge applied to the plates, you should be able to apply the correct electric attractive force to suspend the small oil drop against the pull of gravity. This allows you to calculate the suspending force from the plates. What Fletcher and Millikan noted was that the force is always some integer multiple. That indicates that the amount of charge present is discrete, which the fluidic / aetheric models of electricity cannot account for. With a bit more math and a calculation of the mass of the oil droplet, you can work out the charge on the electron. Although that is not strictly necessary if all you care about is showing the discrete nature of the electric charge.