Hi Kaity,
English teaching is perhaps the most common job for foreigners here in Japan because foreign language instructors are in such high demand and because it is a job that (often) does not require a high level of Japanese competency.
Other jobs are of course available to those from outside of Japan but generally work outside of the teaching field requires fluent if not native level competence in Japanese. So please bear that in mind. If your not fluent yet, keep using JPOD and it won't take too long
I did a search on
http://www.gaijinpot.com/ which is a popular website to search for jobs open to foreigners in Japan but I unfortunately received no results.
I also tried
http://www.academicjobseu.com but again no results were returned at this stage for psychology related work in Japan.
You might like to refer to
http://www.services.unimelb.edu.au/careers/student/overseas/global.html#Japan
This site seems to have an extensive list of job search sites specific to Japan. You never know, you just might find something. Good luck!