Though I've never been to Japan, I love researching stuff, and I came across this nifty
job search. It seems IT, teaching, and international jobs that are not located in Japan, but under Japanese companies, are the most popular. However, right now, jobs are in high demand and small supply, so not only foreigners and immigrants, but also Japanese citizens are competing more and more for these jobs. It looks like it's gonna be a little tough, but I hope this helps!