From what I've read the Chinese used Japanese silver to stabilise their economy. I'm sure there's probably some trigger for conflict in there somewhere.
The Americans probably could have defeated the Japanese by working with the Soviets and the KMT-CPC to remove them from China and Korea alongside bombing them to oblivion with incendaries and nuclear weapons. And yet they instead planned to launch the largest amphibious invasion in history. Obviously the Americans did not want to annex the Japanese but their goal could easily be that of the Qing: that of unconditional surrender.
Imagine a world in which the Opium Wars happened in 1834 and the mid-1840s, and as a result the Taiping Rebellion has been butterflied. A world where the Japanese have been forced open in 1837 after an alternate Morrison Incident. A world in which they suffer decades of humiliation (including an inconclusive skirmish with the Japanese, perhaps as a result of an earlier Ganghwa Island incident) culminating in a disastrous defeat at the hands of the French and Japanese; bad enough that the Qing know that serious reform is needed, perhaps before 1870. Because of that first small skirmish, it would be easier for the French to force the Japanese into a junior role in any alliance. If it all happens before the Franco-Prussian War, the French wouldn't feel the need to appease the Russians, and in any case, if the Germans and Russians were able to solidfy an alliance this point would be moot. At this point, to counter French influence in the East the British or even the Germans could help stabilise the Qing and grow their naval capacity. A third war could be fought between the Qing (perhaps with small support from Europeans) and the Franco-Japanese, this time with a limited Qing victory akin to that of the Grand Alliance in the Nine Years War or the Soviets in the Winter War; enough to weaken the Japanese but not enough to remove them as a threat entirely. As a result of the failure to put the Japanese down after three attempts and with foreign intervention an ever present danger, a quasi-fascist/revanchist movement arises in the Qing Court that decrees that the only way to remove the Japanese as a threat is to extinguish the state. With a China dedicated to this aim its natural advantages would see it pull out an unassailable lead in naval and war-making capacity, and after a decade or two it would both be in the position and have the desire to annex Japan.