It's an interesting question, and there's many reasons why it hasn't been implemented in India, but it also hasn't been exactly "one child" in China. It was a one child policy for urban Han, a two child policy for rural Han, and up to three or even four for rural ethnic minorities.
From 1975 to '77 India experienced a state of emergency, which was unilaterally declared by the then prime minister Indira Ghandi. This era saw civil liberties suspended, and sterilisation forced upon a considerable number of men. In one year alone 6.2 million men were sterilised. This has left the Indian people suspicious of family planning efforts, which are further blunted by widespread female illiteracy. Nonetheless, since then, most people who volunteer for sterilisation are women. In 2014 there were 4 million sterilisations, of which less than 100,000 of them were for men.
Until the 70s India often experienced famine. So the Indian government was as much concerned with the food supply as the number of pregnancies, and took measures to deal with both problems. During this decade there was a "Green Revolution" in the subcontinent, pioneered in part by Norman Borlaung, an American biologist. He helped by introducing famine-resistant high-yield crop varieties to India, Pakistan, and Mexico. This revolution saw the introduction of agricultural financing, mechanisation, pesticides, chemical fertilisers, and new crop varieties, which together mean that there hasn't been famine in India since, and food security is no longer an emergency issue.
India's fertility rate has also fallen from 5.9 in 1951 to 2.3 in 2011. This is because of many important factors, such as rising literacy, economic growth, higher education, women choosing to delay marriage/pregnancy, and sterilisations.
There has also been a problem with infanticide in China and India, where female foetuses are aborted. A one child policy in India would further exacerbate this problem, given the cultural preference for boys. This makes the prospect even less palatable for Indians.
Right now a one child policy wouldn't be justified, and given the lack of famines on the horizon it isn't a priority. When half of the country defecate in the open, one of prime minister Modi's biggest challenges is to improve sanitation by building "toilets before temples". A controversial phrase to be uttered by a Hindu nationalist. But it shows that as India's fertility rate falls, and food production is sufficient, there is no need for a one child policy. There is however, amongst other things, a need for a one toilet policy.
More generally, fertility rates have been falling across the world - both in developed countries, and importantly in developing countries too, sometimes with incredible speed. Consider this 2009 article from The Economist:
Fertility is falling and families are shrinking in places— such as
Brazil, Indonesia, and even parts of India—that people think of as
teeming with children. As our briefing shows, the fertility rate of
half the world is now 2.1 or less—the magic number that is consistent
with a stable population and is usually called “the replacement rate
of fertility”. Sometime between 2020 and 2050 the world's fertility
rate will fall below the global replacement rate
Today's fall in fertility is both very large and very fast. Poor
countries are racing through the same demographic transition as rich
ones, starting at an earlier stage of development and moving more
quickly. The transition from a rate of five to that of two, which took
130 years to happen in Britain—from 1800 to 1930—took just 20
years—from 1965 to 1985—in South Korea. Mothers in developing
countries today can expect to have three children. Their mothers had
six. In some countries the speed of decline in the fertility rate has
been astonishing. In Iran, it dropped from seven in 1984 to 1.9 in
2006—and to just 1.5 in Tehran. That is about as fast as social change
Consequently, there isn't an immediate need for emergency measures. That however may change if the future food supply is strained, and we return to concerns over a Malthusian trap.