Climate of China during this September ending and beginning of Octobor?

The exact climate depends on which city do you want to go. Generally speaking, it is the autumn in China and the general temperature during that time is about 10C to 15C, so it is cool. They need to take some long sleeved clothes, and if they are afraid of the cold, you'd better preprare some coats for them in advance. It will not always rain at that time, too.
The cool weather make that time the best time for visiting China, so I hope your parents will have a nice trip in China.