Mysore could have pulled it off, I think. From what I understand, around the end of the 18th century under Tippu Sultan they had excellent military organization, technology that was not at all inferior to Europeans', and they conquered a substantial portion of southern India while defeating several British armies. If there had been so further Anglo-Mysore wars after the Mysore victory in 1784, maybe Mysore would have remained independent indefinitely.
As I've argued before, what needs to happen is for the balance of power to be preserved in South India for a generation or so more.
IOTL, it was upset by the French revolution- France lost the ability to play power games in South India leaving the British free to act as regional hegemon.
Lets look at why European trained armies were able to generally beat South Indian ones. This hadn't been the case just fifty years before where the dutch were stalemated in the Dutch-Travancori war. But the late 18th century, Indian armies were fielding artillery corps as large and sophisticated as anything in Europe. Where they lagged behind was in the area of drilled infantry- Indian kings tended to rely more on the shock and awe of artillery but drilled Company troops could advance reliably under fire and this was what tipped the balance often enough.
Now by the late 18th C, Indian kings were beginning to adopt European infantry theory, hiring advisors to drill their royal guards and the like. However, these sort of reforms hadn't been put into place en masse. This was fine so long as the Anglo-French balance of power was maintained in South India but once France became preoccupied with its trouble in Europe, French support for Indian clients dried up, leaving the British free to sweep across South India. Mysore was conquered and the Wodeyars placed back on the throne, Travancore submitted as a vassal and so did Hyderabad.
But given a generation more of power games in South India it's quite likely that Hyderabad, Mysore and Travancore, at least would have been able to preserve their independence.
The North is actually much more likely to fall due to the utter chaos that was going on up there. The Mughals were only nominally there and the Mahrattas were overextended and disintegrating.