I have learned of some services that allow Indians to invest in US stocks. However, does anyone know if short-trades are possible through any of these services?
I don't see why not. If you open an account through an online international broker like InteractiveBrokers, you should be able to short U.S. stocks as long as you have sufficient margin or buy the offsetting call options.
You'll have difficulty doing this on the retail side of trading, on the "professional" side it will be much easier, there are more fees though but this is really just a capital problem.
I'd recommend talking to securities firms in the caribbean. Many reputable US banks have subsidiaries literally miles from the US coast, just to avoid many of the regulations regarding opening bank and securities accounts for foreigners (and americans).
Credit Suisse, for instance, routinely creates products and services in the bahamas, which is just a few miles off the coast of the US. On the electronic side, everything is the same, with all trades clearing through their firms in new york city. (look at the product that trades under the name "TVIX")
HSBC is another large bank with an investment arm that does similar things around the US jurisdiction to provide access to the US financial system without the regulatory hassle.
You'll literally just be a wire transaction and a username and password away from trading.
Back to the point though, these firms would all allow "daytrades"