I got nerdsniped by this quantity, and here's more or less where I wound up after monte-carlo sampling some rabbit holes:

- the Praetorian Guard, famous for having been involved in many a roman imperial coup, varied in size between 4'500-6'000.

- on 18 Brumiare VIII, Napoleon had at least 6'000 men at his disposal.

- modern brigades are around 5'000.

- the smallest successful coups since 2010 have been in Africa, with force estimates of 4'000-6'000.

At least in the pre-drone era, "handful" has quantitatively meant at least several thousand (although it's probably true that any political component would have to liaise with only a few senior officers, and a modern brigade is composed of a handful of modern battalions)

[note that Napoleon's was recursively a coup-within-a-coup; his political partners thought they were the brains and he was the muscle, but events proved them mistaken]