I was able to get a Shinsei Bank Amex right away when I moved back to Japan thanks to Amex's global card transfer program. However, it's been over decade and I've never been able to get any other Japanese card so I recently made a LINE pay JCB card. It's a prepaid charge card that can be used at any location that takes JCB, there's no annual fee, and you get 2% cash back in the form of LINE points which you can use to add credit to your balance unless you want to use those points to buy stickers and Starbuck's gift cards. There are a number of ways to charge it including at the register of any Lawson. One weird thing about it is it doesn't have your name on it. It just says "LINE MEMBER" so I could imagine there might be some issues using it overseas. Also, it doesn't seem to have an IC chip and you can't use it to create an account on JCB's website which means you also can't use it for JCB member rewards like airlines miles.
The main reason I got it is a lot of the low cost Japanese and South Korean airlines don't take Amex and I don't like using my US Visa for purchases in Japan if I don't have to. Especially not smaller purchases like budget plane tickets. Anyway, I thought I'd share this for any of you who are still struggling to get a card here. For the record, I don't work for LINE or own any of their stock.