See, the way a coupe detat works is the leadership is cut off, and another leader takes his place. While the former leader might have a larger army, they can't do anything if they can't figure out how to move or issue orders.
At this point, the person executing the coupe uses his smaller army to great advantage, because he can use his tactical skill to the full, while the headless masses of the former's army can only brawl pointlessly, assuming they just don't panic and run or surrender outright.
Needless to say, this can only work in truly totalitarian forms of government, with power centralized around on a group or one person. It would be fairly impossible to do agains a democratic society, where the power is (..fine, I'll say "supposedly") spread amongst many people and replacements can be found relatively quickly in the event one is killed.