Yes you can easily find such work, but PLEASE don't do it! People can and will take advantage of your situation. If you get caught, you'll be deported for 5-10 years, and there goes your plan to be with your boyfriend.

Guangdong province is very strict about this, especially Guangzhou. Guangzhou is the worst place in all of China to be caught without the proper papers. Next up is Beijing.

It will never happen to me !                                         That's what they all say just before they are fined and Deported

What about an F visa?  How can I obtain one of those?  I know you are allowed to work on the F visa...

An F visa is also not a good idea. Nothing other than a Z visa is suitable for your pursuits. No matter what anyone says, do not go for an F visa to work.

Option 1:

If you want to study at a Chinese university for less than 6 months, you can get an F visa for durations up to 6 months. Anything else requires an X visa and a medical examination. As far as I know, you can only work part-time as an English teacher with an X visa with permission. Whether or not you get permission is up to the school and the PSB. It can be a hit or miss.

Option 2:

Agree to work only if the school gives you a Z visa. They will send you home to get it, or to Hong Kong. Do not work on anything else.

Thank you!