Given the historical rivalry between Navy and Army, the only branch realisitcally capable of a coup would be the Navy, though in Politics, the Navy and Army cooperated quite nicely most of the time in WW2, as both were militarisitc enough to continue the war itself. Military honor and the code of honor were very much alive in both branches, so there only was a very slimm change of such a coup.
If such a Coup woud need to be anyway, it would most likely not be performed by high ranking officers, but more likely by a group from lower ranks, possibly influenced by some form of ideology, such as Communism, as there were some Communist sentiments in Japan before and during the war, though very underground. The esteblishment would not try to do a Coup as that was in violation of their oath to Emperor and State. Even though Yamamoto did differ from Tojo in many ways, he was not the one for a coup, just as in Germany the high ranking generals were not openly supporting the Stauffenberg Bombplot, although some would not mind if Hitler was killed.