In many cases, it is not possible to rent a bbq at the campsite. If your accommodation does not have a barbecue, you should assume that you cannot use one. Sometimes a campsite has central bbq areas, if this is the case at the campsite of your choice, you can find this under the facilities tab at the campsite of your choice.
Sometimes during the season, campsites may change their policies regarding the use of BBQs. For example, during times of extreme drought, there may be a complete BBQ ban in effect.