Are there any online sources of information for (English) Christian families in India?
I'm particularly interested in the first half of the nineteenth century.
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The FIBIS (Families in British India Society) is an excellent starting point. They're a "a self-help organisation devoted to members researching their British India family history and the background against which their ancestors led their lives in India under British rule." You will have to subscribe to access all their data (currently £15 p.a.) but they have good explanatory material available free which can help shape your search.
Another site that may be of use is the India Office Family History Search produced by the British Library based on their own transcriptions.
I suspect you've already located the FamilySearch page pointing to online resources, including the two I've mentioned and also their own collections of records.