The signs at the campground say that you are limited to a single night if you are able to find an unbooked campsite. There are no FCFS sites. The ranger station signs also say that there is no overnight camping anywhere within the Chiricahuas except within the Bonita campground.

Any sites that have not been booked at least one day in advance become first come, first served (FCFS) for that night. But no sites are reserved FCFS. So if all campsites have been booked at least one day in advance, then there are no FCFS options at Bonita Canyon Campground.

No, but outside the Monument, to the south there are a few campgrounds as well as some dispersed camping. There is a first come CG at Cochise Stronghold to the west as well as another dispersed area. In addition there are 3 or 4 small first come CGs on the east side of the Chiricahuas as well as some dispersed camping options.