Can i change the type of visa during my stay in china?

Yes, you can apply for a S type from the entry and exit administration bureau. You should submit your application at least seven working days in advance before your L expires. An invitation letter from your wife, marriage certificate and valid temporary Accommodation Registration Form are required. For your marriage certificate, you should get it authenticated by Chinese embassy or consulate in your country. The rules might be slightly different according to the place where you stay.