A toughie, but I think the Bahmanid Sultanate in the Deccan were Shia before the Iranians were if I'm not mistaken. This is a period of Indian history I know very little about though, so I'm not sure how plausible it is for them to spread Shi'ism in the rest of India. If I'm not mistaken, weren't the rulers of Awadh Shi'a as well?