We got an inquiry about mountain biking in Kumamoto:
https://www.facebook.com/Kumamotoi/posts/606689336071169
This has been a topic of discussion on the Kumamoto-i mailing list. Here’s one relevant thread:
https://groups.yahoo.com/neo/groups/kumamoto-i/conversations/topics/10850
You can search the archive yourself to find more information. I know there’s more posts in there about biking in general and I think there’s also more information about mountain biking.
By the way, the information in the Kumamoto-i thread took me to the following page:
http://en.wikiloc.com/trails/outdoor/japan/kumamoto
It introduces some biking trails as well as hiking trails.