Here's the English version of Kumamoto City's page about how to donate. Even though the page is translated the thumbnails you see and the pages they take you to regarding Furusato Nozei (Hometown tax payment) are all in Japanese.

Kumamoto City
https://www.city.kumamoto.jp.e.fm.hp.transer.com/kiji00372174/index.html

Here is a similar page for Kumamoto Prefecture
https://www.pref.kumamoto.jp.e.qp.hp.transer.com/soshiki/27/274572.html?_ga=2.130187023.1891056844.1785999191-797217835.1785999191

And for Yatsushiro City
https://www.city.yatsushiro.lg.jp.e.xl.hp.transer.com/bousai/kiji00326782/index.html

As I look at these now, it occurs to me that it may be difficult to donate from outside of Japan. Not sure about that at this writing.

-- Kirk