I still have a South Central Conference handbook from my senior year in high school (1966 - Franklin Community).
Among other information it provides, is the conference history up to that point. I remember the conference having nine members until Jeffersonville joined in the late 1950s as the 10th member; then Southport left after the 1963/64 school year and was replaced by Bloomington in 1964/65. I think BHS was chosen over University, Madison and a couple others (New Albany and North Vernon maybe?)
A couple of forgotten members of the conference going wayback were Greencastle who was a charter member but withdrew in 1949 and Indianapolis Washington who joined in 1938 and left in 1942.