Is Possession Of A Firearm On School Property Ever Legal?

Yes (under some circumstances).

Under South Dakota law, any person (other than a law enforcement officer or school sentinel) who intentionally carries, possesses, stores, keeps, leaves, places, or puts into the possession of another person, any firearm or dangerous weapon, in any school premises, vehicle, or building is guilty of a Class 1 misdemeanor.

However, this firearms law does not apply to starting guns used at athletic events, firearms or air guns at firing ranges, gun shows, and supervised schools or sessions for training in the use of firearms. The law also does not apply to the ceremonial presence of unloaded weapons at color guard ceremonies.