Not many cyclists enjoy riding in rain. You may wonder exactly how much rain you may encounter in Japan. This depends on when you go and also where you are as Japan is a large archipelago stretching in latitude.
The climate of Japan is cold in the north, temperate in central regions, and almost tropical in the southern islands. Overall, the rainiest areas are the central-western part and the Kii Peninsula in Honshu, the entire island of Shikoku and the central-southern part of Kyushu affected by the summer monsoon.
The least rainy area is the northernmost island of Hokkaido, where the annual rainfall drops below 1,000 mm.
In Tokyo annual rainfall averages nearly 1,530 millimetres (60.2 in) compared to 557.5 mm in London.
A lot of rainfall takes place in intense downpours during a fairly short period of time, typically during rainy season in late June/early July and typhoon season in September. Actual number of rainy days are fairly small.
When it rains in Japan, it just rains a lot then stops completely. In contrast, in England for example, it seems it is raining all the time. Not a lot but bit by bit like you are in a mist sauna (but not that warm), whereas in Japan you are more likely to go in and out for a quick shower with a powerful shower head.
My advice is avoid the rainy season except you go to Hokkaido. Once you are in Japan, check the weather forecast to choose days when you want to cycle. When the forecast is for rain, you may prefer not to cycle, but do something else such as reading, shopping, eating, onsen, etc.