It's true the registration is becoming a bit harder, but you should still manage provided you have a local address and some proof of this. It's certainly a lot easier if you can register the SIM in the name of an Indian colleague. For such low data use, any of the cheap prepaid SIM packs will serve you. In Mumbai, you have a lot of options such as Airtel, Vodafone as well as the large state-run telecom firm (called MTNL) who were the first to offer 3G services in Mumbai.
I would suggest looking at the forum Indiamike.com. In particular, have a look at this sub-forum:
Electronics in India - India Travel Forum | IndiaMike.com