musikit,
Again I know it is going to be a post that only says "I believe," but let me see if this helps at all. I am not a lawyer though.
It is true that Japanese city halls do not issue "marriage certificate" (
kekkon shoumeisho) per se. This is because for Japanese nationals (or for marriages where one partner is Japanese) the fact of the marriage will be written into the
koseki - family register - that an official duplicate copy of
koseki suffices as a certificate.
However, they do issue "Certificate of acceptance of report of marriage" (
kon'in todoke juri shoumeisho) saying that the city hall has accepted the report of marriage you've submitted. This is issued sometimes to Japanese couples as it takes a day or two to record the marriages into the
koseki, so in the meantime this serves as proof of marriage.
But anyway, all that the Japanese authorities issue is this "certificate of acceptance of report of marriage."
This is a blog by a Japanese who got married to an American, and they seemed to have had some issues with the Immigration authorities in Japan over whether their Japan law-based marriage needed to be reported to the US authorities AGAIN in order for the US national to be granted some kind of resident status in Japan.
In this case, she got this letter from the US embassy (addressed to the Japanese Immigration office):
http://www.geocities.co.jp/SweetHome-Green/3497/letter.htmand she got a notarized translation (into English) of the "certificate of acceptance of report of marriage," a format of which is mentioned on this page:
http://www.geocities.co.jp/SweetHome-Green/3497/romarriage.htmThe format was at the US Embassy/Consulate, this blog says.
I know that this is not addressed TO the US authorities, so it might not really help directly, but this might help to establish to the US authorities that this is the only certificate that Japan issues, and that once it is a valid marriage in Japan, it should be accepted as valid in the US as well.
Good luck sorting things out.