That's a tough one. My serious answer is probably getting in contact with and arranging a direct transfer to Shahar Avin, who has done some unusually high-EV research there (disinformation, counterintelligence, and information monopolization causing a civilization-wide cascade of epistemic failures, including impacting EA and AI safety). For example, the Ukraine-related infowar has created an equilibrium that basically gives both sides a free pass to reintroduce large-scale torture of civilians, there's tons of ways that information asymmetry brings big people out-of-distribution and introduces incentives to hurt little people.
I don't think there exist effective channels for big, abstract issues. Any useful intervention must be specific and targeted. You MAY be able to find some "lynchpin" specific issues to work on (or fund), which will shift the larger equilibria and make some progress on the larger issues, but even then the actions are on a specific.
This is compounded by difficulty in measuring or observing changes in the abstract, so such charities tend to drift based on Goodhart's law toward visible-but-ineffective projects.
My recommendation is to pick a specific tyranny that you think can be marginally improved with your effort. Keep your eyes open for others, or for ways to increase the scope of impact, but stay specific in your goals.
Any useful intervention must be specific and targeted.
I did not mean to suggest I was looking for a charity labeled something like "The Tyranny Prevention Center"; rather, I was looking for something that is to anti-tyranny efforts as the AMF is to global health and development efforts.
Ukrainian Army, e.g. Army of Drones. They're a funding-constrained little guy fighting back against a big guy who's also one of the world's top few tyrants.
I think this is probably an example of a really ineffective intervention on a per dollar basis, given how much money is being spent already, unless it's to some organization filling gaps Ukraine's MoD isn't filling
Fight the tyrant, not the Russian army. I believe the sort of thing that the OP is asking for, if we restrict ourselves to just Russia for the moment, is: is there any way to assist with getting rid of Putin, reducing the harm he causes, or preventing the next Putin after he's gone? Focusing in further on the first of those: Is it helpful to donate to democracy-enhancing initiatives in Russia? (Is it possible to help get Putin voted out? The answer is apparently no.) Can one help to get him overthrown? It seems possible, if he were to become unpopular enou...
The first question I would ask is what situation currently has the most powerful people most harming the most meekest people that the fewest people are paying attention to. It seems possible this is the Uyghur genocide. But I learned about this passively and with not that much fidelity, so possibly something else fits the bill. This also wouldn’t take into account future preventions of not yet extant tyrannies.
Specifically: Big people hurting little people. Where can I get my largest bang per buck? I could donate to generic libertarian organizations, but I don't think they fight the generic brand of tyranny I want to fight, and my guess is that most of them are ineffective.