Can't.
Foshan Nanguo Taoyuan is a local 4A-level scenic spot in Foshan, so the management is very strict. You are not allowed to go in and have some barbecue. Moreover, the scenery in this park is very beautiful, and eating barbecue in it is a great scenery.
It will also damage the environment and is undesirable.
BBQ restaurants near Nanguo Taoyuan in Foshan City include Wuyuan BBQ Ground, Huijiang BBQ Ground, etc. You can go to these places to eat.