I worked as a personal tutor for two sons of a wealthy family in Shanghai for a summer. It was great, and paid for my two month long summer in China and Thailand. I got the job through a personal referral though.
China is hungry for foreign teachers, and you can find plenty of jobs in all the major cities (Shanghai, Beijing, Guangzhou, Hong Kong, etc.).
This website has a ton of jobs posted for foreign teachers wanted in China.
https://www.echinacities.com/