There were no notable incidents during the occupation itself, but there were both before and after. A large group of military officers tried to violently prevent the surrender announcement from being broadcast. In Atagoyama, Tokyo, a small group of young people killed themselves after hearing the announcement, and in Matsue, a city in Shimane prefecture, a nationalist named Isao Okazaki convinced several dozen conspirators to dynamite or burn major buildings in Matsue including a radio station, and demanded that the radio operator broadcast their message rejecting the surrender announcement; he refused. One person died, a passerby who was mistaken by police for a conspirator.
Probably the most serious coup d'etat attempt after the war was a decade after the end of the occupation, in 1961. A group of former Army officers plotted to occupy the National Diet and execute the heads of major labor unions, the Communist Party, and other left-wing leaders. This is called the "Sanyū incident" (三無事件), after the name of the secret society which is said to be drawn from the Tao Te Ching, although the exact meaning of the phrase is murky. The chief conspirator died in the courtroom in the midst of his trial.
This was a volatile time in Japan and left-wing students were also attacking Americans at this time. At one point the ambassador's car was swarmed by students and he was stuck for hours before being rescued by helicopter. Eisenhower decided not to visit Japan because he was warned his security could not be guaranteed.
During the occupation itself there was nothing this serious; this was due to the national mood which had recognizably turned against the military and left a power vacuum for the Americans to fill. Of course, the occupiers were concerned about right-wing backlash and it played a role in the decision not to prosecute the Emperor.
Like DuelingKeytarBears said, there weren't organized movements, or at least big organized movements. I quoted this French study, that looked at newspapers of the time and military journals, that shows the number of incidents between 1945 and 1960. In this case incidents is a very broad category, so a fight in a bar over a girl counts as much as a plot to assassinate MacArthur, with arson, sabotage, supply train attacks and protests against the Japanese government also being counted.
https://www.lpthe.jussieu.fr/~roehner/ocj1.pdf
The numbers are:
Apr-1946: 3,800
May-1946: 3,200
Jun-1946: 2,700
Jul-1946: 2,600
Aug-1946: 2,700
Sep-1946: 2,400
Oct-1946: 2,100
Nov-1946: 1,700
The numbers, according to the authors, are similar to those seem in Germany and in the cases of lesser crimes, to seem in bases in Australia and Iceland. Violent cases according to the 8th army report of 1947 were about 12 a month for 1946.
Only in three cases could the resistance be called "organized": in February 1946, with newspapers saying that the Black Dragon society trying to plot against GHQ, and in April 1946 there was an alleged plot to assassinate General MacArthur, organized by a group led by general Hideo Tokayama, and in May 1946 a vigilante group was discovered taking action against US soldiers. They didn't span the whole country and were dispersed very quickly.
News of the Tokayama plot in The Times:
https://trove.nla.gov.au/newspaper/article/68973490
Most of the times the incidents were throwing rocks or assaulting soldiers while they were off-duty, confraternizing with Japanese women. There are also incidents of soldiers abusing the local population, with cases of robbery and fraud, and retaliation against it.