The OP could be achieved by a few things:
- Neighbouring Christian invaders conquering India rather than Muslim rulers. This would be helped by a No-Islam scenario where the faith is butterflied away to not exist.
- The Christian conquerors not being able to expand west, and not being completely destroyed by another invading force from the east, allowing them to focus all their efforts eastwards on India
- The Christian conquerors aggressively evangelising, rather than the laissez faire approach of the OTL Muslim rulers.
- The Christian conquerors maintaining a single polity over all of India (North and South), rather than the fragmentation that occurred under the Muslim dynasties. This unity would accelerate the evangelising above
How about this scenario:
Islam does not exist. The Arab expansion still happens due to population and resource pressures in the Arabian Peninsula, but it is via several disjointed migratory waves by different and feuding Arab tribal confederations like the OTL Germanic migrations, rather than a single unified conquest like the OTL early Islamic conquests. These Arab tribesmen overrun swathes of the Byzantine and Sassanid Persian Empires, but fail to wholly conquer either. Syria, the Levant, Egypt, Libya and the rest of North Africa as well as most of Anatolia is conquered from the Byzantines, while Mesopotamia and parts of the Caucasus are conquered from the Sassanids. Due to their disunity and haphazard migratory waves, the Arabs will fail to break into the Iranian Plateau, where the Sassanids linger on. These conquering Arab tribesmen settle in the captured regions and Christianise over time (especially those that settle in former Byzantine territories), establishing independent Arab Christian Kingdoms.
In the west, these Arab Christian Kingdoms are linguistically and socio-culturally a mishmash of Hellenistic, Roman, Syriac, Coptic, Berber and Arabic influences. Later on, the Byzantines will somewhat recover and retake some of their lost territories (including the entirety of Anatolia) from these Arab Christian Kingdoms, but will not reconquer all of them.
In Mesopotamia and the Caucasus, these Arab Christian Kingdoms are linguistically and socio-culturally a mishmash of Hellenistic, Roman, Mesopotamian, Persian and Arabic influences, but are likely to become some form of heterodox (probably Nestorian) Christian. The Sassanians will try to recover and retake their lost lands from these Nestorian Arab Kingdoms, but they will be hit from the east by a large, powerful and warlike migratory confederation of Nestorian Christian Turkic tribes (much like the OTL Seljuqs). These Nestorian Christian Turks topple the last Sassanian vestiges and conquer all of Iran and the Nestorian Arab Kingdoms that were established in Mesopotamia and the Caucasus. The conquest of the Nestorian Arab Kingdoms goes fairly smoothly for the Nestorian Turks as they are coreligionists, but they face stiffer resistance as they try - and fail - to push west against the Byzantines and western Arab Christian Kingdoms. Unable to overcome this western resistance, the Nestorian Turks settle down to rule over their new empire, which encompasses Iran, Mesopotamia, the Caucasus, large parts of Central Asia and all of the Eastern Arabian coast (granting them control over the whole Persian Gulf). Over time, all of these regions become heavily Nestorian, encouraged along by aggressive evangelising efforts by the Nestorian Turkish rulers. However, whilst their empire is religiously Nestorian, it is also linguistically and socio-culturally a blending of Turkish, Arabic and Persian influences (much like the OTL Turco-Persianate Muslim dynasties).
Unable to expand westwards, the Nestorian Turks turn east and begin sending raiding parties into India, which over time grow into full scale invasions. Often, the Nestorian Turks also divert - using a combination of bribery, intimidation and force - their migrating Turco-Mongol kinsmen from the steppes southwards into also invading India, avoiding their depredations upon their own imperial Iranian heartland. (Due to butterflies, Genghis Khan and the Mongol Empire do not exist ITTL). These migrating Turco-Mongols are fervently Christian, especially because of long exposure to their Nestorian Turkish kinsmen, and view their invasions of India as holy crusades to Christianise the region.
Thus, the Christian Turco-Mongols conquer all of India in several successive waves, even as the Nestorian Turkish Empire in Iran begins crumbling due to internal stagnation and external pressure, which only sends more Christian Turco-Mongol warriors flooding into India as refugee-crusaders. Eventually, a Christian Turco-Mongol dynasty arises that encompasses all of India (like the OTL Mughal Empire at its height). These Christian Turco-Mongols are much more zealous than their OTL Muslim counterparts and impose a thorough evangelical policy to Christianise their Indian Hindu subjects, seeking to emulate their Nestorian Turkish kinsmen who successfully Christianised Iran and Central Asia. If they have sufficient zeal and manpower (which is reinforced by continuous waves of Christian Turco-Mongol migrant-crusaders), over time they will grind down Indian Hindu resistance and Christianise the majority of India. This is how India ITTL becomes majority (likely Nestorian) Christian.