An obvious prerequisite for a Japanese conquest of China is the conquest of Korea. As NFR observed, it didn't play out too well in OTL, but another option would have been a gradual dynastic alliance between the Koreans and Japanese. The obvious problem is that Ming China would keep an eye on developments in the Korean peninsula, so the Japanese would have to go out of their way to make a show of submission to the Dragon Throne. After the early 1600s, once China feels comfortable with an ostensibly compliant Nippo-Korean "vassal", one may imagine the Chinese appealing to the latter to buffer the Empire against the rising Manchu threat; later still, as popular uprisings weakened the Ming, the Nippo-Koreans may be called in as the Manchus were in OTL to restore order, and, like the Manchus, overstay their welcome.
Now as Martel writes, it's difficult to imagine a Japanese emperor ruling China from Japan. It's simply too risky to give the job to anyone else, lest he decide to ditch any loyalty to the Nippo-Korean crown and set himself up as the founder of new Chinese dynasty. So the Japanese emperor would have to move to Beijing along with all his retinue. The rest of the story is easily guessed: within three generations the ruling elite has been thoroughly Sinicized and regards Japan as a quaint ancestral homeland, nice to visit every once in a while, but of little political interest. And just as in OTL, Manchuria has become the Chinese provinces of Liaoning, Jilin and Heilongjiang, so in TTL Japan may likely end up as the provinces of Jiuzhou (formerly Kyushu), Benzhou (formerly Honshu) and Beihaidao (formerly Hokkaido)*. As for Korea, it would be the province of Hansheng.
* I'm just transliterating kanji as though they were pronounced in Mandarin.