I've never heard of such a thing. To some degree it misunderstands the Japanese feelings about Hiroshima and Nagasaki. While there was (and still is, somewhat) an embrace of a "victimhood" response (which has been criticized as being an awfully convenient way to avoid talking about Japanese atrocities towards its neighbors during the war), it is not an aggrieved form of that. I have never seen any impulse of even being "owed," much less wanting revenge, with regards to the Hiroshima/Nagasaki bombings. If anything, the Japanese have consistently expressed that while Hiroshima and Nagasaki were tragic, they were not incomprehensible — not signs of US "evil" or anything like that.

There have been Japanese terrorist groups, but most of them seem to have been involved in domestic struggles. The Japanese Red Army did level some attacks at American institutions (e.g. foreign consuls) in the 1970s, but that's the only instance I know of a Japanese terrorist group even specifically targeting the United States for anything.

Part of this no doubt has something to do with how the Occupation worked out. The US didn't really do anything terrible to the Japanese after World War II. They ruled with somewhat of a heavy hand in the early days, but on the whole the result was to help turn Japan into a modern, strong democracy with a world-class economy, and to reassure Japan that they would have little to fear from Maoist China, Soviet Russia, or their proxies. The US allowed the Emperor to stay on as a religious figurehead, if not a political entity. It worked hard to ease the transition and to keep the Japanese from being exploited by political extremists in their rebuilding period. As a result US-Japanese relations have been surprisingly good considering how terrible the war was. (They have had their ups and downs, of course, but on the whole, surprisingly good.)

It is a situation utterly different than the sort of relationship that the US has with the Middle East, as a point of comparison, where the US is seen as an occupier, an invader, an aggressor, an exploiter, a support of dictators, and so on.

Are you more interested in a short term retaliation like the immediate years following the war? Or any period of time including up to modern day?

People now generally misunderstand what the the atomic bombings meant at the time to people living in Japan.

Conventional and fire bombings were more of an issue. 215 cities had been bombed, 105 badly enough to be designated for centrally led "War Damage Restoration Planning" after the war (p. 1, 18 of that book). The firebombing of Tokyo alone killed about as many people outright (130,000) as both atomic bombs combined (105,000 - Remember, in the early days and weeks, nobody knew what the long term death toll from radiation exposure would be [closer to 200,000 in the end]). Recent work on the Japanese decision to surrender has also suggested that the Soviet entry into the war weighed more heavily than the atomic bombs on the minds of Japanese leaders making the decisions. In other words, horrific as we now know them to have been, they were less important in context (to Japanese people outside of Hiroshima and Nagasaki) than they are in retrospect.

The atomic bombing did not really become a flash point in national consciousness until 1954, when issues of radiation and ideas about American wrongdoing were brought to the forefront of public debate by the Lucky Dragon Incident (Japanese fishermen got radiation poisoning from fallout from the Bikini Atoll hydrogen bomb test because the US miscalculated the safe distance). For example, between 1945 and 1949, the government denied any special status to either of the atomic bombed cities, and only approved special reconstruction money for them when Hiroshima appealed directly to GHQ, and GHQ pressured the Diet to approve the "Peace Memorial City Construction Law" because they thought it would be a good PR move internationally (detailed in Hiroshima mayor Hamai Shinso's autobiography - Also note that Hiroshima made a point of keeping Nagasaki out of the first law, and Nagasaki had to come back and ask for their own funding law. So much for solidarity). Moreover, until the occupation ended in 1952, information about the exact nature and effects of the atomic bombings had been largely suppressed in Japan by both the wartime government and GHQ, so it took the shock of the Lucky Dragon Incident to even make people go back and take another look at what happened with the atomic bombs.

Long story short - no, nobody was talking about revenge for the atomic bombs, because most people either didn't know about them, didn't understand them, or cared more about the conventional bombings that had an objectively greater impact on their lives (unless they happened to be a survivor of Hiroshima or Nagasaki). More than that, most people cared about surviving: there were horrific food shortages in the early years of the occupation, and people had been almost on starvation rations even before the war ended. The general populace only started to harbor strong feelings about the atomic bombs as a distinctly national injury in later years, and by that time Japan and the US were very closely linked as Cold-War allies.

On the day the bomb dropped there were about 2 dozen American POWs in Hiroshima, all captured fliers. We don't know their exact numbers for reasons that will quickly be explained. They were being held about a half mile from the Aoi bridge, the target of the Enola Gay. All but 3 were killed instantly by the blast. US Navy pilot Normand Brissette and Army gunner Ralph Neal crawled into a cesspool to escape the heat. 2 days later a B-29 ditched off the coast of Hiroshima. They were taken to a jail in nearby Ujina. Army radio operator Martin L. Zapf was among them. He later gave this account:

He put us in a civilian jail for a couple of days. We met two Americans in the jail who had been … POWs in Hiroshima when the bomb was dropped. Actually, there were twelve Americans in Hiroshima and all of them were killed. These two boys survived. One was a B-24 gunner from Okinawa and the other was a Navy flyer of some kind, I think, also, a gunner. They both died while we were with them for a couple of days, because they were, [it is] difficult to describe what they looked like. They had pus running out of their mouth and ears and nose and they were in agony. They wanted to die. It was terrible and we, of course, couldn't do anything for them. We didn't know what had caused their appearance. It was terrible. Anyway, those two boys died while we were there.

The Americans asked repeatedly the Japanese doctors to do something. "Do something?” one of the doctors finally replied. “You tell me what to do. You caused this. I don't know what to do.” The next morning both mercifully expired.

Now, I told you that story mainly so you'll understand this one. We don't know the name of the third survivor. We don't know his rank or position. We don't know where he was from or what his rank was. If Brissette and Neal knew, they were too busy screaming and begging for death to speak about it.

An onlooker later said he had "blond hair, green eyes, white waxlike skin, a big body, and very strong looking like a lion"

"He was the handsomest boy I ever saw”.

The mourning after the bombing a mob tied him up to the Aoi bridge.

They were probably unaware of the irony.

They pinned a note to his chest.

“Beat This American Soldier Before You Pass.”

The onlooker said he screamed and begged for mercy while the mob clubbed and stoned him to death.

They didn't seem to particularly care.

Sources:

http://symonsez.wordpress.com/2010/07/29/the-forgotten-tragic-loss-of-american-airmen-at-hiroshima/

http://www.thenation.com/blog/162596/hidden-history-american-pows-were-killed-hiroshima

http://oralhistory.rutgers.edu/interviewees/30-interview-html-text/55-zapf-martin-l

http://books.google.com/books?id=y9YKrRM1BowC&pg=PT276&lpg=#v=onepage&q&f=false

http://books.google.com/books?id=h2tgdlDFtYwC&pg=PA351&lpg=PA351&dq#v=onepage&q&f=false