The Kingdom of Mysore was one of the memorable independent polities in India, starting at first, as a vassal of the Vijayanagaran Empire until its collapse in 1565, then as an independent state until becoming a vassal of the British East India Company, and later the British Raj until 1799 until formal annexation into the modern state of India in 1947.
So with a PoD between 1565 to 1799, have the Mysorean Kingdom exist as an Independent state to the Present day. Bonus point if Mysore can manage to maintain it's greatest Territorial extent (as of 1784)
The first Anglo-Mysore War ended in 1769 with a peace treaty that required Mysore and the Company to come to each other's support if attacked by a third party. Shortly afterwards, Mysore got into a war with the Mahrattas - it's unclear who started it, but the important fact is that the Company refused to support Mysore and Haider Ali regarded this as a betrayal of the treaty (whether it was or not - it wouldn't have been if Mysore had attacked - is irrelevant, it's how Haider Ali saw it that's important), and this seems to have been a critical event in fomenting Haider Ali's anti-British feelings, which he passed on to his son, Tipu Sultan.
If the Company instead chooses to support Mysore, then it might be possible to avert the growth of anti-British sentiment and preserve Mysore as a somewhat truculent ally/neutral. As British influence expands in the rest of India, the importance of Mysore, tucked away in the far south is likely to decline to a point where the British think it's more trouble than it's worth to occupy rather than merely vassalise.
End result may give a chance, but no more than that, that Mysore passes through the British period with a notional independence that it is eventually able to transform into something closer to the real thing, somewhat like the path Nepal went along at the other end of India.