This undated article regarding one room school houses in Madison County, Indiana features a picture of the King school house, which was located at the corner of 350 W and 900 N. I do not have the date of this article, nor information about what publication it was from.
Sadly, I don't know anything about this school house either. There were King relatives who lived in this area, and I wonder if the school was named for them. Most likely candidate would be George Washington King (1823-1892). On my next visit to the Madison County Historical Society I will try to see what records I can locate.
If any readers know anything about this school, please let me know.