You don't necessarily have to eliminate India, just harass them enough should be fine. If you are lucky enough to get woodsman II bonus you can usually capture some Indian workers which often screws their growth. Pillage improvements (and roads), mess with their workers and you'll get ahead of Dilli's in population.
Same goes for China. Pillage and harass/capture workers as much as you can. Eventually they will send some serious military unit to get rid of your pesky threat, but this delay/change of tactic is often enough to get you ahead of Beijing in population also.
Huh, that does seem to work, though it does seem to require quite large forces. Thanks! I managed to surround Beijing with 4 Warriors, which made it possible to pillage all their food improvements and then pin them down inside the city walls. Beijing's population actually dropped from 4 to 1, due I'm sure to whipping up defenders.
Dilli? ... I still think it's a good idea to send out enough Warriors to sack the place. It can rebound in population very fast, and it's much harder to get to and sit on food improvements. Though I also put 4 warriors around it, and Asoka only had Warriors, he was still aggressive enough that he was able to kill my marauders.
And those religions add a lot of culture points. On turn 94 Dilli had 133% of Babylon's culture points, though I had the Oracle and Dilli had no wonders.
...
@timfi: I've noticed the same aggressive tech trading practices. As near as I can tell, you have to offer the AI techs worth at least 150% of the techs you're requesting before they'll entertain an offer. Absurd offers, like when they'll offer you Archery in exchange for Mathematics, result when none of the other techs they have on hand are sufficiently cheap relative to what you're offering.
I assume this is intentional, to handicap the human player somewhat, but more often in my experience it has the effect of eliminating most tech trading.
EDIT: It still depends to an ungodly degree on luck. For instance, if you use the Stonehenge-CS gambit to pop a GA, you have to gamble on not popping a GProphet instead. (And you have to gamble that Egypt will target the Pyramids instead of Stonehenge.) If you decided to use the Oracle to get Monarchy, you have to gamble that Priesthood won't suddenly become 125 lightbulbs more expensive than it had been. To be relatively assured of reaching techs and buildings in time, you have to skimp on the Warrior stack you send out, which greatly increases the chances that war against either India or China (or both) will go very badly.