Really? Oh, really?!
There are quite a lot of options defining which shape things can take, depends on skills of both parties, so as design of actual structure, what can they produce, or which terms/agreements they can make politically wise.
As @o.m. correctly pointed out - it a city level figth, and there are examples in history of such events when ruling class was overturned or changed. From ancient time(Rome), trough modern time(orange freedome, yellow wests, capitoliy etc)
So it does not need that much of a fire power, like it hard to call it a war, it more like a rebellion, a coup.
It can be like a compeition between swordsmen, or all willing vs all willing a sword figth, or a fist figths on the streets etc
It can take all kinds of forms. Being in space adds aditional dimension to that city scenario, giving ability to do things by controling software(hacking) and some key point hardware, if there is any by design.
Or it can be just one(few) guy shouting promises on a public square for 3 month's and 1% active power hungry population, reluctance of the rest, making a win for new power.
There is really no rigth or wrong scenario, and weapons required(as displayed by examples) almost none in some cases, fists are enough - and it not something as not probable or a minimal set, but it quite working scheme in reality, so as it possible to say it has certain degree of be fair, a version of democracy - fist democracy.
what it means being in space, in O'Neil
mm, not sure I should word it that way, and good stuff can be written in the setting you presented in the q in the way you ask about, buuut, it smells like an old stuff, generation ships, degradation and conflicts there, not that good old is bad, but it was early time on thinking on all kinds of things, in time when a digital drawing was not known and wasn't a thing(in 50-70's)
Since then a lot has changes, and someone has to reinvent what such a conflict may be on a cylinder, what kinds of solutions there are, because of the goal of expedition(setting on a planet), what it means to set a self sufficient colony with modern tech thus defining what do they have.
- in that sense your question lacks what do they have
I mean if you just need action scene of the conflict to be, some passing by event, you do not need much really - fists and handguns are well enough to start and achieve results in a coup - it all you really need - it easy, fast effective, no way to kill the station.
But if your whole story, half of, good portion of it - is about that conflict, or you investigate the potencial and possibilities of problems and solutions in this setting - then it would be a too shallow of a take on what's available to the guys, in a sense of options.
- in a sense there is no limits - "that nuke we did carry to melt ice caps on the planet, remember?, so I did fix it and I have it, also I placed a random guy who constantly shouts allhuckhackbar next to it, locked in a room, on this optimistic note let's start our negotiations - you talk to me now, or you talk to him later if you lucky enough." There is no need for a random guy, it can be a detector and a random event - needs an open system which can be understood, and be verifiable and can be seen in action which places certain percent probability of total destruction, and is eash to understand. So you can use what you have - if it is a big gun which makes a big hole in the shell - it can be part of the cards one plays. So in that sense it pointless to ask what can or can not they use - it all about how do you play the cards you have - one can have nothing and win, one can have everything and lose.
Being in a cylinder, next to a planet which has some potencial to be inhabited(meaning it big enough, and has some sort of atmosphere, maybe some water), in a space it really changes what can be done, expands it.
In short, or a biggest thing is that they can expand, build more of cylinders.
And they can split without figth, for a start. And then they can attack each other and destroy cylinders if they like to do so.
Even if there are tensions, which go trough a whole population, like dems and reps in usa, they can work on common goal, like splitting, making second cylinder or few of them.
And being in space, next to a planet mass, means they have means to do so(not taking mass form surface of planet(but it can be an option), but taking mass from upper parts of athmosphere (atmosphere scooping) for reactive mass for their probes, which can bring asteroids if there are problems reaching surface of the planets because of some limits of what they can implement rigth now)
Heading to a planet to colonize it, it also means bringing technology tree in some form, of dravings, description of processes, how to manuals, a plans to enroll and later recreate that technological self sufficiency, seed installations(which even if destroyed can be recreated, they aren't thag big or complex compared to a cylinder).
Losing competences in the technologies in space means death - if one can't serve the station(if there is no smart matter) then sorry, your life line is out in a decade or few no matter what you do - you have to get some tech competence back in this time.
And having comptences means a lot of things can be done in space if materials are available.
Basically 6 out of 8 planets in our system have moons, which can be source of materials, even small moons of mars are actually huge chunks of materials technology wise and they are huge as what can be done from them.
Asteroids in a system they also can be such sources of materials. (Basically you can bring the whole asteroid of materials minus oxygen by means of that asteroid, what it has, to a planet, if you need it)
So answer your q is that there is no limits, but fists and guns is welle enough. But if you set just for that, it will be a waste of conflict in such setting, space gives you a new dimension, so as capacities of them which are result of their initial goal are way bigger than just that. But most likely it a coup which ends in few days, and regular people do not care or even do not know that much about it all.
Reading some of your comments, I can't comment so add some stuff here.
Really forget tanks airplanes vehicles and war action of bunch of stuff in this setting. A colony, what it need the stuff for, a colony is just a big city. It even hard to imagine a significant rupture of society in this curcumstances, when everyone understand that they depend on everyone, it a survivial situation. It easy to convince that conflict on large scale is death for them all, and hard to convince it to be a solution, if they understand the situation which they are in.
Power struggle happens behing close doors - it has benn so for ages, and coups are failsin that sense.
The system is not capable to support a war even if imagine they have few tanks for some reason. Few lucky shots and all the capacity to make or repair them is gone. Not talking that few heavy vehicles in a city, in a war setting, not a such a brilliant idea, nor does it bring something of value really. (But depends, killdozer did well enough)
As a compeititon of some sort of arena figths, with some rules it can be a thing actually, if you like to have archaic approach. In a sense one wanna risk his life and bring death to his opponents(or maybe it not death, maybe a lose of dice rolls is convincing enough and can quench his attitudes) - okay here is your chance, those who win and survive define this or that matter, rest of the public relictantly allows this on that matter, because we see your resolve and our resolve to oppose is defiently not that big.
It may become a system, a part of managment. But really it up to you to invent it to depict it, if you have what it takes, as it is your story and there are many ways. But yes, changes in societal norms and conducts may happen, there is nothing strange in that, people to adapt, and despite the wars majority of our systems are in place to prevent them, as wars are way too expensive and it a last resort, and letting steam out on constant basis can be a thing and was a thing in time when duels were more of a norm, so it not something unheard of, or not something which had not been done in a bit different way.
A rule of good life - one devides, another chooses - you can do this or that, you choose.
Also another rule - when there are more than 10 cylinders, and it means it easy to have them, then you surrender, successefuly defend your self, or bust. In this situation a cylinder is not such a big commondity or big asset, or a value. There is no point to spare it, when you remove opposing actors. With a star system resources you can have them as many as you like, if there is no one who disturbs you.