I'm not an expert on the imperial factions, but the I.S.B. always seemed to be the most heavily indoctrinated and loyal to the empires ideals. I think therefore they would be more willing to follow one leader,and there agents could easily silence any dissenters within their ranks. While the Moffs, Inquisitors, and Admirals are to power hungry and would quickly tear the empire apart.

I don't know what Imperial Intelligence is, but they sound like a power hungry group.

^Well in that regard, of which you are correct, wouldn’t it follow that they’d be the least likely to perform a coup since they’re die hard Palpatine Loyalists?

^I thought about there loyalism being a problem but I think by the context of the question the coup will be a given, and I think that the I.S.B. would be willing to follow someone else who embodied the ideals of the Empire if they became disenfranchised with Palpatine by discovering he was a sith.

The Moffs and Grand Moffs directly control the systems. They can easily take regional forces and the planets.

^ Conversely, the Grand Admirals/Generals (although it's mostly Admirals; there's only ever been one Grand General and it's Tagge) have direct control over the Imperial Military

I'd say they stand the best chance of actually accomplishing a coup

However this begs an interesting question: Does Vader count as part of the Imperial Military? Like, is he an official member of the hierarchy?

Canon suggests he sort of... isn't, considering he gets ordered around by both Tarkin and Tagge during and after the Battle of Yavin, though that probably changed by the time of the Battle of Hoth

The Inquisitors.

I laugh every time I read the Essential Atlas when its the Dark Empire chapter, and it says that Sheev approved of the infighting cuz it was "culling the weak". lol

Inquisitorius- in canon, no way they could take out Vader and Palps

ISB- possibly, not sure they'd have enough influence. The other branches don't seem to care for them

Intelligence- barely heard of them

Moffs- maybe, they'd probably fall apart

Generals/Admirals- If Thrawn was involved, 100%. They probably have the best chance of success otherwise

Inquisitors are great, but Malachor showed that they only possess a fraction of Vader’s power—and I’m sorry, but I can’t even see Vader taking down Palpatine in a coup. Grand Admirals & Generals, strictly because Thrawn.

ISB for sure they even spy and report inquisitors they’re also feared in the Empire so they’d have a good chance.