The country in question is small, more like a single city than a sovereign nation, fear-wracked, and under the imposition of a fascist matriarchy. The country exists in roughly the early Middle Ages. My protagonists (two people) do not desire power, only to remove the government. What would be the best way to get them to convince others to rebel?
There are so many ways to incite rebellion, but in general find out what people are most fearful or angry about and who they are suspicious of, then blame the latter for the former, while insinuating that the government is protecting them.
If you want them to be less evil and go after the government directly it could be harder depending on what sort of the reputation the leaders have, sometimes oppressive people are popular (ex. Vladimir Putin).
There probably needs to be more information to really provide a detailed answer, but other common tactics include provocations, sabotage, pretending to be the rightful king or queen, accusing the ruling class of having a different religion or not believing in the dominant one, accusing then of not being real members of the nation (if they have some foreign parentage)
Idealistically you can go the way Gandhi did. Point out the inequality. Explain how the suppressed feel. Again and again repeat how things should be instead. Be prepared to do jail time for your convictions.
If the protagonists are locals, if everyone in the city knows one another, if you really can hold out, this may lead to a peaceful solution. Courage required. Martyrdom decidedly possible.
Fundamentally, all civil wars happen because a significant segment of social structure either falls outside government control or thinks the government is too weak to stop it from getting outside government control. Rebellions sometimes can rise from desperation (typically famine but religious or ethnic persecution works) and if the government fails to contain the rebellion can lead to civil war.
Sometimes when you wish a change of government a credible threat of civil war or rebellion is sufficient. Even without actual threat. When Gandhi demonstrated that the British can't actually make the Indians to comply with their orders, if Indians simply refuse, the Indian independence became inevitable. The British could have used force (or further force), but that would have essentially forced a wide spread rebellion and the cases where forcing the population to rebel against your rule makes sense are pretty rare. (It does happen, suppressing a rebellion is good cover for removing large numbers of inconvenient people or stealing lots of property.)
That said, normally you do not do a regime change by inciting a civil war. It is inefficient and unpredictable. And since "inefficient" invariable means "causes death and destruction on a massive scale" it is especially inappropriate for anyone who presumably cares how many people die. Trying to start some sort of armed rebellion also has high risk of being killed by government forces and by definition requires close association with violent and desperate people with sharp, pointy objects. It might even involve prolonged periods of "healthy outdoor life". Or long periods of not being able to go outside due to armed guards and locked doors. And most importantly, this is important enough to mention a second time, the results are unpredictable. The only sure thing is that your plan for what happens after you win will not work. Someone who is good with adjusting their plans on the fly might manage to do so, but people like that do not need to start civil wars.
The second best option is what Gandhi and others did in India. Convince the old regime to give up the power without a fight. In India this was relatively easy because the government was foreign and giving up and going away was actually cheaper than fighting for it. I think that ease was the reason Gandhi went for it despite rather obviously being aware that India would be divided along religious lines with high risk of bloodshed. Probably he also expected to use his influence to moderate the violence. Who knows?
In any case, the problem with this is simply that you do not control what happens after the regime change. Nobody does. For the very simple reason that the new regime starts from zero and has very limited ability to control the events. Even in optimal case the new regime will have less power than the old regime did. And yes, that is the same old regime that had to give up power because their position was untenable. The shift still makes sense since the old regime was losing power while the new regime will be able to increase its power over time. But the first decade or so will be unstable and unpredictable.
If you decide to use this option the basic strategy is to start a social process that erodes the power base of the regime that it isn't practical for the regime to stop. If there is a reasonable method for the regime to retreat with honor and security they will eventually do so. The greatest difficulty, which Gandhi did not really face since the British could simply leave, is to protect the old guard after the regime change.
In South Africa, the obvious black leader was someone the apartheid regime could trust to understand the consequences of "payback" and do what could be done about it. This created a situation where giving up power while Mandela was alive and could take over was a better choice than waiting until the shift was inevitable and taking the risk with "not Mandela".
And that is a hint for the even better option, which is simply to engineer a situation where it is in the interests of the regime to hand over the power to someone that they trust and that you can trust to follow your plan because they are already fully committed to it. When can this happen? As in South Africa, if it is inevitable that the position of the regime will weaken in the future and there is a person available with solid power base that the regime can trust more that its own future prospects, it becomes beneficial for the regime to negotiate a power transfer deal while its negotiating position is as strong as possible. Which means right now.
The exact methods vary based on what the power base of the regime is, but the general approach would be to help the regime contain a power base that it is suppressing because it can't control it due to some fundamental issue. A matriarchy would have problems controlling the political power of men and would suppress any such power, for example. Which would lead to violent protest and even terrorism. So a man who uncompromisingly advocates gender equality thru changing the laws not breaking them would make an acceptable transition leader. If you assume several people in conspiracy, you could have several such people apparently competing for influence while actually cooperating based on a premeditated plan. This false division would make the negotiating position of the old regime appear stronger than it is and push them to make the transition sooner.
You also need a second prong to make the position of the regime deteriorate. You can use passive, non-violent, resistance. Violent resistance may actually make the regime stronger and always makes the country unstable and political process unpredictable. You can use external pressure from other countries. But the best approach is to have somebody inside the regime who is for all appearances fully committed to the matriarchy and loyal to the point where the rest of the matriarchy think she is too strict and rigid about it. Then simply loyally support someone significantly older than you with more power than competence. In most oppressive regimes that describes all leaders. If you are loyal enough you can inherit the power.
If the regime is based on the children inheriting the power of their mothers, as is quite possible in a matriarchy, you can groom the daughter to be either your puppet or a willing collaborator. If you have the trust of the mother she will generally consider you to be a good influence and actively support such grooming. She does not have the time and somebody has to guide the child or she will be lost to irresponsible sycophants or people paid by the mothers enemies. True and easy to point out even before a daughter actually exists, so that the mother won't even remember who decade ago told her that raising the daughter should be left to someone who is proven to be loyal.
In any case once you have access to leaders, it is fairly easy to support decisions that look solid and even brilliant, but cause the power base of the regime to erode in the long term. Most leaders of oppressive regimes, regardless of intelligence, have blind spots large enough to float a battleship thru. And the cut-throat competition within such regimes strongly promotes short term thinking, which should hide indirect sabotage thru decisive action to protect the regime quite well.
The inside position is also useful to make sure that undesirable male leaders are less successful than the ones collaborating with the plan. Conversely the male collaborators can make certain that the female collaborators are more successful with dealing with the male issue even when implementing obviously stupid ideas. At that point it becomes expected that the female collaborators will push the issues they are strong on. And have agents and informers inside male organizations. This provides good cover.
At this point I should admit that I have totally lost track of what I was trying to say. And whether I succeeded. Hope this is useful to someone.