Japanese banks are
horrible about giving credit cards to foreigners. In my third year working for a big 4 accounting firm in Tokyo (having lived in Japan for 5 years), I walked into Sakura Bank (where I had my savings account where my monthly salary was deposited) to apply for a credit card. At the time, they were having a promotional campaign giving credit cards to
students. Well, three weeks after my application I got a rejection letter. So they were giving cards to students with no job and no income but they would not give a card to a foreigner with a full-time, long-term job at a worldwide accounting firm. This treatment of foreigners is simply inexcusable.
I'm not sure what to tell you. I was also rejected for two other cards (one of which was an ANA Visa card: one of several reasons I don't like ANA

)
I finally got my first Japanese credit card two years ago (after having lived in Japan for nine years and just after having bought a house here. I guess they thought if I was good enough to get a home loan then I'm probably safe for a credit card

)