Well Travancore, and Hyderabad are fairly easy since both wanted independence anyways, ditto for Kashmir (but they only assented to Indian dominance because they feared being dominated by a foreign power). Madras is more difficult since it was close to the Pan-Indian movement, but if say India suffers from a violent civil war versus Ghandi style independence you could possibly see a split between the Northern and Southern rebels, Madras is the only difficult one foresee. Mysore is a tad more iffy since it's ruler at the time assented to become part of India and it would probably again take a nasty civil war to push them away from India.
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Travancore did not want independence. That was the work of the Diwan of the state. The people there wanted to be Indian.
With a POD in 1930, trying to split India is way too difficult. It is definitely a POD in the 1880s that would really help drive home a split on the subcontinent.
Pakistan was by no means an inevitability, so it wouldn't just pop up out of nowhere. If there is separatist tension throughout India, then that goes equally for the states that would be Pakistan.
And quite frankly, that was the only movement that had any real momentum- and it was one that only became absolutely certain in 1947, with Mountbatten in charge.
None of the Princely States will be getting any guarantees of security from Britain. They appointed Mountbatten with the purpose of getting out as quickly as they could so when the blood was shed they wouldn't be charged with it. Wavell was more for a cautious approach; he would have probably taken it to 1948 as slated.
One possible POD is 1911. Instead of moving the capital from Calcutta, and rejoining Bengal, the British Government of India chooses to stay. Calcutta was considered remote for the pan-Indian nationalists, so they met in Bombay. Bombay would continue to develop as the epicenter for the nationalist movement, while the Government of India ends up more focused on the Calcutta-Madras-Rangoon triangle.
National sentiment rises, but because the split of Bengal had a lot of Muslim support, there begins to be voices wanting to create even more provincial autonomy. The Presidency Armies are not organized into one Army of India. As a result national sentiment gets more violent- while agitation in British India is easily handled, in the Princely States, it is met with a different reaction. Soon the States begin to fully develop their own state apparatus, building standing armies, and modernizing their police. This won't happen everywhere, but you'll see it in Hyderabad.
War of Independence starts, and the more moderate faction in Madras (given the lighter hand in that Presidency, along with more support from pan-Dravidians) sticks with the British. Several Princely States join the British side, and the fight ends up in a split with some Indian States being independent, some being annexed, while Burma might split off, along with Madras. So basically, India in Malê Rising is the most you can really split the subcontinent.
Ultimately by the late nineteenth to early twentieth century, there was too much of a common feeling towards a united India, at least in the elite circles. But the elites were smart, and they courted public sentiment through both agitation and legislation. And throughout history, elites tend to lead revolution. This was helped by the fact that throughout EIC rule, it was ultimately said that the goal was to help set up India as its own country, led by men who were 'brown in colour and blood, but English in taste'- and in many ways, that's exactly what happened. The book 'India in Transition' from 1932 details that now those men appeared, Britain was afraid, they weren't quite ready for it. Similarly 'India at the Durbar' written in 1911, said that the ultimate goal of British rule was to prepare India as an equal partner in the British Empire, as the other Dominions were.
TO prevent the Union of India, you really need Britain to administer the place differently. With a POD in the 1700s, you can prevent the Governor of Bengal from exerting any power over the GOvernors of Bombay and Madras. With a defeat by the Sikhs in the Anglo-Sikh Wars, you can probably see the survival of one more Indian state as a way to block pan-Indian nationalism from forming. But ultimately once all that land is consolidated and administered as one place- once the people are brought into the administration and business of the country-even a little- the seeds are sewn for a united Indian state.
EDIT: Also, most of India's intelligentsia was Bengali; the notion of their own state literally only surfaced as a result of Partition, as a way to mitigate the damage of splitting Bengal.
