There seem  to be multiple tags on that topic besides amenity=bbq, see tourism=picnic_site with multiple specifications concerning bbq/fire, and leisure=firepit. What fits best should be determined by your local knowledge.

I am very happy to help, of course, but may I suggest you to bother your search engine of choice for a list of possible OSM taggings next time...? (No offense!) That is what I had to do myself for all the suggestions above as I haven't mapped anything related yet and have no clue about those tags either. In addition, according to your track record, you seem much more experienced with OSM than me... Just get it done ;)

Cheers!