Should I go to Aso-Kuju in September?

Is it a good idea to visit Aso-Kuju National Park in September? Does it rain heavily? Do you also know whether visiting Yakushima in September is a good idea? How many hours does it rain daily?

According to YES Yakushima (YES- Yakushima English Service), The month of September is the 5th rainiest month:
https://yesyakushima.com/yakushima-weather/

September is considered to be part of “typhoon season” in Japan, although sometimes the best weather occurs right after a typhoon. (But also sometimes a typhoon causes damage such as landslides that can close trails or make them hazardous.) But it can rain (or snow) in Japan, sometimes heavily, even during months that are considered the best for traveling.

The best you can do is make flexible plans and be prepared for the fact that rain could interfere with outdoor activities. This is tougher for Yakushima than for Aso-Kuju. Once you get to Yakushima you are basically stuck there, but for Aso-Kuju you can pick a base to stay where there are appealing things to do on a rainy day or you can get in your rental car or hop on a train and go on a rain-proof day trip somewhere. For Aso-Kujo a rental car is a big asset in getting to trailheads anyway.

It’s good you are at least thinking about these things. I’m afraid that some people plan detailed itineraries with no consideration at all given to how rain might affect them. On the other hand, some people are afraid to even come to Japan at all during June because they have heard that it is the “rainy season.”

You can get some idea of average statistics on the following page (maybe pick Fukuoka and extrapolate; in general Yakushima will be somewhat rainier), but nobody can tell you whether it is going to rain on any given day in September, let alone for how many hours.
https://www.japan-guide.com/e/e2273.html

If you have the chance, and especially if you have a car, then Aso & Kuju are great places to see. You'd be too early for the autumn colors in places like Yabakei, but they still look quite nice. And yes, there will be some rain. As for Yakushima, as they say, it rains 8 days a week. It is typhoon season, but people tend to overblow this way too much online. You may have to deal with some, but they are not going through every other day like the hyperbole shouts.
https://goo.gl/RwpnU8