Agreed. But you'd need a Zanzibar wank where Indians can be a plurality in Zanzibar, and the Sultanate gains independence separately and evolves into the Indian version of Singapore. You can have a 20th century Zanzibar wank without this, but to make Zanzibar Indian you need more Indians.
The African mainland is a lot harder, unless you want a city state like Mombasa, Mogadishu, or Kismayo. Zanzibar is definitely the easiest. I would add Arabs to the people who would be helpful in this state, since at least in Zanzibar there were quite a few (not least of all the Sultan of Zanzibar, who I'm assuming for the most likely chance of Zanzibari success must be effectively powerless and led by Lee Kuan Yew-style Prime Minister). As mentioned, white African immigrants are useful, if you want a Singapore-style state. Maybe more whites fleeing Kenya in the 1950s?
In any case, such a state can absorb Indian migration from elsewhere in East Africa (especially if there's Idi Amin-style ethnic cleansings going on).
I've mentioned Zanzibar and Singapore a lot, but a key difference is that the Indian population in East Africa was always more fragmented than the Chinese population in Singapore. Maybe something like Lee Kuan Yew's Speak Mandarin Campaign, to improve links with India? I don't know which language you'd pick, though. Probably Hindi, since it's India's main language, even though most Indian East Africans spoke Gujarati or Tamil. Could be cool if the government chooses a non-Hindi Indian language, although perhaps unlikely. In any case, English will be the main language of this state, due to the links with India and Britain.