Thanks a lot guys for all the suggestions and options! I think since I already have the United Miles, I will try first calling United as suggested and give them the continental airline flights that I see on the CO website and see if they can book that for me.
I will also apply for AA credit cards as those seem to be better than getting the delta airlines card. I hope AAmerican CSRs can do a good job of getting a flight all the way to BLR via alliance partners in case the United option does not work out.

I never thought of calling and asking them. Thanks a lot for that heads up!! I assumed that whatever is available online is the only option we have. This is very good to know