Andy-
A lot of what I know about Douglass comes from Johnny Green, Jr., a former pro at Coffin. His dad was the longtime pro at Douglass, and Jr. grew up in a house next to the pro shop there. He tells me that the property was donated specifically for a park "for negroes", and that the couse was originally laid -and- maintained by local black loopers at other courses who wanted a place of their own to play. He says it started with three tin cans buried in the ground, and then grew to a proper 9 hole course in an overhaul from an architect whose name escapes me (I'll call him in the next couple of days to get the name again). That design work was in the 30's.
I can't say -and probably shouldn't have implied- without specifically checking that Douglass was segregated by rule or law, but you probably well know that the culture of Indianapolis in the 1920's would have been an extremely strong disincentive for whites who might have been interested in playing there then; de facto segregation worked in two directions at that time.
Green tells me that the other munis were "whites only", at least for the early years of Douglass. In fact, he specifically mentioned Coffin, which was interesting because it -absoluetly- had a largely black user group by the time I started playing it in the 80's. And as you mention, it was a UGA stop. It was also the locarion of some -very- big money games between black golfers in the region for many years. I don't know when it was desegregated, but the richness of the African-American history there suggests it had to have happened fairly early.
I don't know the circumstances behind many of the other munis - South Grove is really, really old - 1900ish, and Riverside used to be Highland CC before it moved to Its current location. I'd be stunned if both didn't begin segregated.