The word elaphine means of or pertaining to a stag. Therefore, stag nights, stag parties, stag dos, stag drinks, stag weekends and all such hideousnesses could be rebranded elaphine nights, elaphine parties, elaphine dos, elaphine drinks and elaphine weekends.
I feel this would somehow make them better. At least it would make them sound better, which is a start. Elaphine paintballing is such an unwieldy combination that people might notice that the activity just isn't any fun. If it were we would be doing it all the time.
Elaphine derives, since you ask, from the Cervus Elaphus or red deer.
An elaphine painting