[Icelander]

Intelligence Analysis* to determine whom it is necessary to arrest, Administration to organise the personnel and resources to do so in a smooth fashion, Tactics if there is a risk of resistance or escape and Leadership to make sure that everyone actually performs the job to which you assign them (with Politics, Propaganda and Public Speaking being possible replacements or supplements to that depending on whether the characters legitimately hold any power or not).

Politics, Propaganda and Public Speaking continue to be vital to ensure that the coup or counter-coup is viewed as legitimate. Law is pretty much irrelevant, except as a Complementary Skill to these.

Administration, to keep everything functioning even after arresteing key leaders, will obviously remain important.

*Other investigative skills can come into play here, but assuming that the PCs have some underlings who report to them, Intelligence Analysis is probably most appropriate for making determinations about whom it is absolutely necessary to arrest immediately, either to prevent them from seizing control of the state apparatus and/or to allow you to replace them and do the same.