One could imagine a possible attempt at a Chinese conquest of Japan at any time where China wouldn't be hard-pressed by nomads and had somehow taken a naval turn. OTL these conditions were really only fulfilled under the Yuan Dynasty. That said, there are periods in China's history where naval aggression occurred, the Liu Song/Sui invasions of Champa being the prime example.
In terms of alt-hist scenarios, your best bet would be a more expansionist Song/Ming Dynasty that has somehow reached some political accommodation with the Mongols (maybe an extended heqin policy with a Mongol state that could control its underlings). Additionally, for this scenario to work you don't want China conquering the steppe like what Han, Tang or Qing did, since that shifts China towards a more continental focus.
Alternatively, China also has a history of 'filibustering' its neighbors, with various Chinese migrants or second/third-gen Chinese attempting to usurp political power in various Indochinese states (Taksin in Siam and the Ly (arguable)/Tran Dynasties in Vietnam). There's also 'roving armies' like Koxinga or Mao Wenlong whose power was enough to establish semi-independent polities of their own. So a successful Chinese invasion of Japan doesn't necessarily have to be done through state means.
In terms of actual naval ability, a sea-focused Chinese state really doesn't have too much trouble reaching Japan. The routes were already well-charted by the time of the Tang and with the development of the 'junk' sail during the Song it's not difficult for a Chinese fleet to reach Japan within a few days given favorable weather conditions.
In terms of conquering Japan - that's a bit more difficult. The logistics of provisioning such an army would be a great strain on Chinese finances (the Southern Song spent 90% of its income simply on maintaining a defensive navy), so it's a delicate balance between bringing enough troops to actually capture Japanese defences and not bringing so many troops as to bankrupt the state in the process. A large invasion force definitely requires Korea as a staging base: a smaller force can set off from Jeju or the Ryukyus, though Korean acquiescence in the adventure is probably required for any medium-term success.
Historically, the Yuan's 30,000-strong invasion force in 1274 proved insufficient to take even the 500-year-old defences at Hakata Bay, having made little progress while exhausting their own supplies of gunpowder in the process, the latter forcing the premature Mongol withdrawal.
It's quite possible that a conquered Japan could have been partly colonized by China Ireland-style, especially one that eventually develops very strong trade links with China and whose ports become Chinese exclaves, but it's less likely that any Chinese dynasty would actually desire the annexation of faraway, costly and rebellious Japanese land rather than just a simple admission of Chinese suzerainty by the Japanese tenno.
