By saying "Green Card" I am assuming you meant a "Visa" and not a working permit? Do you intend to gain employment whilst you are there? Below are requirements and criterias needed to visit Japan:

A visa is NOT required for UK or Irish passport holders who wish to enter Japan for a period of six months or less for the following purposes:

Sightseeing, recreation, amateur sports, visiting relatives, inspection tour, participation in unpaid lectures or meetings, study, attending a conference, business contact or other similar activities. Journalists travelling to Japan for a short business trip do not require visas.

On arrival at immigration in Japan, such a passport would be stamped for a stay of 90 days. This period of stay may be extended for a further 90 days upon application to an immigration office once inside Japan, but approval is at their discretion.