What certificates/medical are required to fly in Japan?
With a US license, you are allowed to fly US registered (n-registered) airplanes everywhere in the world. 
Find a US CFI (in Japan) that can get you current and start flying. 

The bigger problem might be, to find a Medical Examiner in Japan that is allowed to do medicals in Japan. My first search, at the FAA website (https://designee.faa.gov/SelectTypeOfSearch/SelectTypeOfSearch), didn't show anything. 

Not sure if BasicMed works for you though.