Joe Tomei here. If anyone hasn’t gotten their jab, the prefecture has opened a vaccination center (Moderna) at Gran Messe (near the airport expressway entrance) for anyone who has a coupon This is the reservation link https://www.covid19-vaccine.mrso.jp/kumamoto/VisitNumbers/visitnoAuth/

The hours are weekdays 6pm-9pm and weekends noon- 6.

Mike Rupp, in the comments, writes about the Vaccine Passport

You go to the Kuyakusho, and they can give it to you at the window where they do Japanese passports. You need to bring your passport, the proof of 2 shots (the sheet with stickers) and you must write down a date for which you plan to travel on the form. It took about 15 minutes for me [Mike] and I was the first foreigner.

Mike’s timeline has a photo of his document but unfortunately, I can’t add it to this post ($%&’&$ Facebook) and we’ve blocked photo comments ($’%&#%& trolls on the Internet), but if you ask him nicely, he may help. If you aren’t sure of your Japanese (or even if you are!) having a photo of the object of your desire can really help things along.