Here's a screen shot from "The Hawk of Powder River" (1948) showing the church at the southern end of Iverson Village, along with a large rock behind it (Church Rock, for lack of a better name) that has been helpful in determining where the village was located. The area where the town was built is now part of a trailer park off Topanga Canyon Boulevard, just south of the 118 freeway.
The Western town was built in 1945 for the Gary Cooper movie "Along Came Jones." It remained more or less intact and grew over the years, being used in a number of movies and TV shows through the 1960s. Inevitably, it met the fate that seems to befall all Western movie towns: It burned down.
The church wasn't around in the very beginning but appeared early on. I've heard a theory that it was mobile and was put in place whenever the producers wanted a church in town. Personally I think it probably just existed for a certain period of time and if one were to track the movies in which it appears, one could approximate the years that made up its lifespan. (Update: New information has surfaced on the history of the church since this post. Check it out here.)
Trailers now occupy the former site of Iverson Village, but that same Church Rock can be seen still marking the spot. The slightly shorter rock to the left of it is Gumdrop, which is an even more reliable marker that appears in a lot of movies, identifying the southern end of town.