There are provinces which can legally employ those sixty or over, if they are physically fit, a big concern, and the primary reason why most cannot and do not hire those sixty or more. Guangdong Province is out, unless one is already firmly entrenched.
I have been led to believe that some places can get a Z visa for those who are very fit, in spite of the laws, which tend to actually be guidelines in some cases. Yes, second and third tier towns and cities have more liberal rules sometimes. As mentioned by another poster, there are some which advertise for teachers up to 65, so don't give up! Good luck.