I'm curious what positive articles do people think the NYTimes could carry about India? Keep in mind that being a US based newspaper, human interest stories about positive contributions by individuals outside the US are very unlikely to make it into a US based paper. What usually works is a wide systematic positive story, often through the lens of a few individuals.
When India was growing rapidly, and basically created a massive new middle class in the 90s on opening its borders, the NYTimes had a lot of positive stuff to say (Friedman, of The World is Flat fame, was one of the biggest promoters of India). This was a massive positive systematic change, that was covered widely.
But since then what positive systematic changes does India present that would be useful for an audience halfway across the world to know? There are a ton of individuals doing amazing work in India (and note, even this article focuses on the strength and bravery of individuals who fought the system) Indian institutions are famously terrible, and are getting worse. Frankly, the only possible positive stories that you could do about India that come to mind are the rapid rise of solar energy (however, all of that is in the planning stage at the moment...we need to see how it materializes). That's pretty much all I can think of.
Frankly, India doesn't help itself by screwing up situations we could have used to build a better image. You bring up Australia and sports. China did the Olympics, and it was an amazing spectacle. It truly changed people's perspectives of what China was capable. India had an opportunity to do something similar with the Commonwealth games (although that would understandably be ignored by the US media anyways)and that was a massive disaster which only served to emphasize how terrible and corrupt our institutions are.
Edit: I think the NYTimes could do a really great positive (and relevant to the US) article on the Indian Electoral Commission. They basically moderate the elections, and have done a really great job in ensuring largely free and fair elections in a chaotic country which is otherwise awash with corrupt institutions. It's actually pretty amazing that India has maintained and strengthened democracy in the past ~70 years, and the EC has a huge role to play in that.