You would have to be a full time student. I believe you have to put in so many hours to obtain that type of visa. It will probably restrict you from finding a real job although you might get some luck in finding part-time work. 

First off, I don't recommend doing this. Anyway...

I know in Beijing's Wudaokou area, there is a Korean-run Chinese school that does this sort of thing. Students can go to the Chinese lessons, but they don't receive grades or any sort of degree. Many of the "students" in fact only sign up with the school to get an X visa, which they use to stay in China to work illegally or "chillax" or whatever. Needless to say, it's pretty expensive (3000 RMB for a  3-month X visa  when I last heard about it a few years back). Chances are it's gotten more expensive since then if it even still exists. 

I'm guessing that similar schools exist in other major cities (particularly near universities that attract a lot of foreigners), although I think you'd be better off going to a visa agency in China or Hong Kong to get an F or L visa instead (if you can even still do that; it's been awhile since I've checked). Or you could fly back home and apply for a 6 month or 1 year  tourist visa.