Hi jana33.....check out thebeijinger.com  the personal/job ads on there.....or better yet post an ad of your own saying what your looking for.....I see plenty of Chinese people on there who offer tutoring and will usually travel to most parts of Beijing.

The going rate I've usually seen is 100rmb an hour but you could probably find people that are cheaper or more expensive as well.  When my gf did Chinese tutoring she charged 100rmb an hour which included class + homework assisgnments and she helped the students pick out a book for them to use for studdying/class.

Ni Hao!I'm a local Beijing girl offering private Mandarin lessons to expatriates and their family members as well as crash courses to short term travelers. I have been teaching for over 6 years both as a private tutor and full time teacher attached to language schools. My schedule is flexible and I charge reasonably. I use my own study materials but will also be happy to tutor from your textbooks if you already have them.I am based in the east of Beijing so I prefer students in the following areas:-CBD/Guomao, Sanlitun, Dongzhimen, Sanyuanqiao, Chao Yang Park and Qing Nian Lu. Also, anywhere along subway line 6. Email me for details: dengbrown@gmail.com