The Stagecoach originally called a mud wagon, was used to transport passengers and freight between Caliente and the Kernville area.

When the movie Stagecoach, was in its planning stages, the producer asked John Wofford if he could provide him with a stagecoach for a scene crossing the river.  Wofford who regularly provided extras, horses, equipment and cattle to the movie industry said he could do that.  So he modified the mud-wagon and make it look like the stagecoach needed for the scene.

Incidentally, it had been called the mud-wagon because passengers sitting on the exposed seat would often received a share of the mud thrown from the wheels as the magon moved along. 

The stagecoach as you see it here is the modification made by Wofford and is the stagecoach as seen in that Kern River crossing scene with John Wayne on the back, snapping his whip and yelling at the horses.