This is Atsuko.
I'd like to share a page from the Governor of Kumamoto Prefecture that provides information about gas stations.

Please stay safe, take care of one another, and avoid unnecessary travel if possible. (*•̀ㅂ•́)و✧

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On the evening of August 1, information became available online about gas stations that are operating in the Yatsushiro area and throughout Kumamoto Prefecture. If you have been affected by the earthquake, please use this site to find nearby gas stations that are open. More stations are expected to resume operations in the coming days.
Kumamoto Prefecture is working together with the national government to secure a stable fuel supply. Knowing which stations are open may help everyone feel a little more at ease and avoid unnecessary rushes to refuel.
For those affected by the disaster (from Japan's Ministry of Economy, Trade and Industry):
Even during power outages, some gas stations equipped with emergency generators are able to continue providing fuel. Information on the operating status of these stations is available at the link below.
Service Station Search (including emergency fuel stations):
https://www.enecho-ss.meti.go.jp/b/enecho/