http://www.visainchina.com/familyvisa.htm
This should tell you what you need to know including eligibility but it doesn’t look as if you would get one unless you are talking foster care and even then you might not be a close enough relation unless you have been appointed by a court as a guardian (just guessing here).
A student visa might be another option for an extended stay. Once again you will not be eligible to take paid work. That’s not to say that it isn’t easy to get work but if you are caught then they fines can hurt and it may result in repatriation or even imprisonment.