Suppose that they had realized back then that electricity was going to become one of the most important technologies humans have in the future and decided that they should make a major effort to figure out the direction of the charge so future generations wouldn't get stuck with the wrong convention. All the top scientists, engineers, inventors, and crackpots in the world try to come up with some way to tell.
Was there some method reasonably within their reach that would have worked?
I'd guess the first thing they would try is weight. The body gaining the charge carriers should gain weight and the body supplying charge carriers should lose weight. That would probably fail because the mass of electrons is very low, and I don't think they had anything that could resolve weights that small. (I'm not even sure we have anything now that can do it).
The second approach might again use weight, but with the realizing we don't have to measure what the weight is, just whether it has increased or decreased. So take two weights that are as identical as you can make them and put them on a balance. Seal the balance in an airtight container to prevent random air currents from disturbing it (or pump out the air--the vacuum pump was invented around 100 years earlier), and put it someplace very cold and with very little temperature variation, and adjust the masses until the balance shows no apparent movement for months. Then charge one of the masses and see if the balance can still remain apparently still for months. If it can't, and consistently goes out of balances toward the charged side conclude that side probably has the charge carriers. If it consistently goes toward the other side conclude that the charged side gave up charge carriers.
I think that this too would probably fail. The mass difference is too small and isolating the balance sufficiently from outside disturbances is probably too difficult.
Could they produce a stream of charges in a vacuum? Let's say they can. Considering the material they had to work with if those were negative they would probably be electrons and if they were positive they would probably be atoms or molecules with a missing electron.
They would probably quickly discover that streams of charge in a vacuum are deflected when they bring a magnet near them and figure out that lighter charged things deflect more. They would then discover that all the negative charge streams they produce have carriers of the same mass, but the positive charge stream carries have different masses depending on how they are produced and they all have mass much greater than that of the negative carriers.
I think they might lead them to conclude that the negative charge carriers are the fundamental ones.
If they even had a corpuscular theory of matter, they might have considered weight. But this was firmly back in the Enlightenment "Natural Philosophy" kind of thinking when materials were "imbued" with properties like gravity and levity or heat and cold. Some of the people working on these things also had a keen interest in alchemy and the search for a philosopher's stone.
Part of the problem we have in trying to put ourselves in their minds is that some or most of their reasoning is unrecognizable to us as "science." If you try reading EG Newton's Principia Mathematica it's laid out in prose from first principles using geometry and is essentially unrecognizable except with a strong education in Euclid.
Thermionic electron emission in a vacuum tube would let you distinguish between electron and element: the electrons are liberated much more easily then the source material and result in current flow through the circuit.
This lets you build diodes as a result, so assignment of electrical direction based on that phenomenon would get it correct.
EDIT: in fact with a cathode ray tube you can literally visualise charge direction from looking at a foil wheel being spun in a vacuum: https://m.youtube.com/watch?v=K2G6M3cYJZs
Was there some method reasonably within their reach that would have worked?
I'd guess the first thing they would try is weight. The body gaining the charge carriers should gain weight and the body supplying charge carriers should lose weight. That would probably fail because the mass of electrons is very low, and I don't think they had anything that could resolve weights that small. (I'm not even sure we have anything now that can do it).
The second approach might again use weight, but with the realizing we don't have to measure what the weight is, just whether it has increased or decreased. So take two weights that are as identical as you can make them and put them on a balance. Seal the balance in an airtight container to prevent random air currents from disturbing it (or pump out the air--the vacuum pump was invented around 100 years earlier), and put it someplace very cold and with very little temperature variation, and adjust the masses until the balance shows no apparent movement for months. Then charge one of the masses and see if the balance can still remain apparently still for months. If it can't, and consistently goes out of balances toward the charged side conclude that side probably has the charge carriers. If it consistently goes toward the other side conclude that the charged side gave up charge carriers.
I think that this too would probably fail. The mass difference is too small and isolating the balance sufficiently from outside disturbances is probably too difficult.
Could they produce a stream of charges in a vacuum? Let's say they can. Considering the material they had to work with if those were negative they would probably be electrons and if they were positive they would probably be atoms or molecules with a missing electron.
They would probably quickly discover that streams of charge in a vacuum are deflected when they bring a magnet near them and figure out that lighter charged things deflect more. They would then discover that all the negative charge streams they produce have carriers of the same mass, but the positive charge stream carries have different masses depending on how they are produced and they all have mass much greater than that of the negative carriers.
I think they might lead them to conclude that the negative charge carriers are the fundamental ones.