Thinking about it, a simple model for rebellion might have the following stages or chain:
General
1: Backdrop of injustice or detachment
2: Incident of realisation
3: Small conspiracy of like minds
4: Minor acts of opposition
5: Publicity or Propaganda
6: Recruitment of malcontents or radicals
7: Major act of opposition
8: Recruitment of the masses
9: Public protest
10: Major civic opposition – probably violent
11: Regime change, installation of new system or leader
Trying to apply it to your scenario
1: Backdrop of injustice or detachment
Their obviously has to be something not right with the Prince in the first place, he might have a reputation for being harsh, cruel, or decadent etc. This should probably be something distasteful to the common man but not completely unreasonable to the Princes piers or the society that he functions in.
2: Incident of realisation
This would be the moment when the rebellions founder finally could take no more. It would probably be something very personal to them that they could not overlook or ever forgive, and they believe it is wrong in every way. A classic example would be something like after months of overtaxing the persons village beyond their ability to pay the Prince himself orders the burning of the persons farmstead and the imprisonment, forced labour, or execution of the persons family as an example of what happens to trouble makers.
3: Small conspiracy of like minds
This stage would be the person seeking out others in his position, people sympathetic to his new cause, or radicals to aid him (maybe with their own agendas).
4: Minor acts of opposition
Once a small team is assembled they would look to start making trouble for the Prince. These first acts would probably be reasonably minor and be carried out in such a way as to make the Prince look foolish, weak or expose his faults or flaws.
5: Publicity or Propaganda
The next stage would be publicising the achievements of the previous acts of opposition in the hopes of fostering the sympathy and support of a greater population. Interestingly the Princes efforts (and failure) to capture or bring to justice the opposition group will also help to spread the word amongst the common man.
6: Recruitment of malcontents or radicals
With increased publicity and renown the opposition group would then be in a position to swell its ranks by recruiting from the greater population.
7: Major act of opposition
To really boost support and encourage more people to flock to their banner the opposition group would need to perform a major act of opposition in order to firmly establish themselves as a serious movement. This might be kidnapping the Princes right hand man, directly attacking the Princes residence and burning it down (poetic justice maybe), breaking into and releasing all prisoners from the Princes jail or labour camp, destroying one of the Princes businesses or revenue streams etc.
8: Recruitment of the masses
With a very public and major act of opposition under their belts (and no doubt the Princes extreme reaction) a major proportion of the population would be open for general recruitment and talk of downfall for the Prince would be on everyone’s lips. At this point revolution is almost inevitable and it would take severe and very decisive action from the Prince to turn the situation round.
9: Public protest
With the majority of the population on board the opposition movement would just have to get them out on the streets, probably marching on the Princes palace in one giant (and angry) mob. All along the route rabble rousers would be giving speeches working the crowd up and keeping them on mission.
10: Major civic opposition – probably violent
There is only one thing an angry mob is good for, and that’s rioting and swift justice. It would be likely that the mob would be able to cause mayhem in the streets (easily outnumbering any form of police or personal guard) and force their way into the Princes palace. The ring leaders would probably take this opportunity to storm the palace themselves for their final showdown with the Prince, either killing him themselves, capturing him and giving him to the mob or maybe even capturing him and forcing him to stand trial (though that is unlikely given mob attitudes, and any trial would be short with the obvious swift and bloody justice)
11: Regime change, installation of new system or leader
Once the old Prince has been dealt with the leaders would then have to control and calm the riotous mob and persuade them to return to their homes and become peaceful. They would then have to swiftly install a new leader or government or take control themselves. The weeks immediately following this change would be critical in cementing the change as the population is already primed for violent upheaval and any miss-step or perceived injustice might have them all out on the streets again with obvious consequences.
…then give it a few years and see if a similar thing happens again. History as they say often repeats itself, and once a precedent has been set many more malcontents might start thinking they could do much better.
The above of course doesn’t include for action from the Prince which would make the whole process much more dynamic and complicated.
As to making it all part of one giant skill challenge I’m not sure. It seems mainly like a lot of really interesting roleplaying situations, secret meeting in shady taverns, rousing speeches in village barns, night raids, evading the authorities as they search the streets. You might even get a bit of intrigue at the princes masked ball etc.
You could probably do some of it as skill challenges but I would say most of it would be skill checks as part of the roleplaying during certain events. To me there is a subtle difference, one is mapped out before hand, one is normal freeform roleplaying.
Anyway I hope these ramblings help in some small way.