I used to run the Community Center English program where I live. The boss at the center was told that we were coming back after being away for a couple of years and he put out feelers if I wanted to organize and teach some programs.
They never interfered and let me do as many classes as I wanted and let me schedule classes outside my study room hours. Basically, I was able to fit 4 adult classes and 3 children's classes a week at 1 1/2 hours per class. They paid me 70.000 60.000 won per class (sorry not 70...my mistake). The hours of course changed each year, according to my main teaching schedule...some years another class, some years I cancelled a class. It was great pocket money and lots of fun up until the last year.
I did this for 7 or 8 years (plus morning phonics at a couple of kindergartens) before quitting. They found a Korean teacher to take-over but I think the adult classes stopped because they became grammar rather than conversation. Also, by the time I finished, the new boss was putting his oar in and making everything just a little bit difficult.
I was lucky in scoring this job but I think if you approach your local Gu office or the center's themselves, with a plan or idea, you might be lucky. Also, keep your eye on the local newspaper. Some positions do get advertised. The best bet though is to talk to people and let it be known that you would be keen to do some community teaching.
