If my residency in Japan as a student expires in 2 months, can I still get a tourist visa?

You can call the visa office of China embassy in Tokyo to enquire whether Japanese residence permit (alien registration card) with 2 months remaining validity is accepted or not.

I guess that maybe your application will be denied because you are a student in Japan and the residence permit will expire in 2 months, the visa officer will doubt that you go to China to find a job or overstay.