There used to be a program by the NOVA group, but they went bankrupt, and I cant think of any more at the moment. However this site http://www.gaijinpot.com/ has lots fo information regarding jobs available to foreigners, so you could have a look int that.
Considering you're now out of college, you could perhaps do further studies in Japan if you apply for a MEXT scholarship, which gives you a monthly allowance of 150000yen, and covers all tuition fees. (I'm personally looking into an undergrad scholarship).
In your case, if you were to apply for the postgrad scholarship, you wouldn't even need ANY knowledge of japanese. They'll put you in an intensive japanese program.
My Chemistry teacher studied organic chemistry at university on a postgrad MEXt scholarship. He told me about how he had to learn hiragana in a day, so it must be quit intensive.
Without a doubt though, JET is the most appealing. JET also offers the position of Coordinator for International Relations, so you would be teaching large classes of children. You would be receiving international guests, editing and producing pamphlets in English and Japanese and Advising and Planning international exchange programs. However, about 10% of all JET participants are CIR's, so its probably not the easiest to apply for.
Much of the appeal for JET lies in its relatively low working hours, and very high pay. Just mentioning this because it might mean not all hope is lost ;)
I wish you luck! I wanna go too.... :/