While I can't speak for earlier periods, India suffered numerous famines from 1500 to 1757.

While there are numerous famines in this period spanning more than two and a half centuries, here's a list and description of famines that India suffered from 1500 to 1550.

• 1509 (Bangalore Coromandel):

This famine resulted in many dying of hunger. There was heavy voluntary slavery, children were sold for four or five fanams each. Hindu merchants (called heathens) like Chatis were said to be experts at this.

• 1520 (Deccan to South India):

Military hordes and plunder destroyed the crops causing famine. No relief measures were adopted.

• 1528 (Ahmednagar):

During Sultan Bahadur's campaign against Burhan Nizam Shah I of Ahmednagar the latter laid waste to the country and prevented supplies from coming in, causing famine. Sultan Bahadur retreated.

• 1534 (Kashmir):

In the aftermath of the Kashgari Moghul invasion of Kashmir, there was economic crisis and people were ruined. Still crops were sowed but the harvest failed causing famine. People died and there was an exodus.

• 1539 (Cambay South India):

Due to drought and war in Cambay famine occurred. There was heavy mortality, epidemic and also cannibalism.

• 1540 (Sindh):

Mirza Shah Hunun, the ruler of Sindh upon hearing that Shah Hoomagoon, who had been lately defeated by Share Shah at Lahore, was about to invade, ordered that no crops should be sowed. A severe famine lasted for three years.

• 1544 (Parva Area):

Shortly after the arrival of the Jesuit Francis Xavier on the fishing coast of Parava, in south west india there was famine. Christians supplied relief.

• 1550 (Kollam / Coulam, Malabar Coast):

This was a general famine which resulted in extreme scarcity of life.

Sources.

• Duarte Barbosa (trans. Mansel Longworth Dames), "The Book of Duarte Barbosa" (vol. 2, 1921).

• Lt Col A.T. Etheridge, "Report on Past Famines in the Bombay Presidency" (1868).

• Ferishta's History of Dekkan..(Vol. 1). Jonathan Scott (trans.).

• R.K. Parmu, "A History Of Muslim Rule In Kashmir 1320-1819" (1969).

• Cartas de Dom Joaõ de Castro, Quarto Vice Rey da India …" (in "O Investigador portuguez em Inglaterra" vol. 16, 1816)

• P. Pierre du Jarric, "Histoire des choses plus mémorables advenues tant ez Indes orientales que autres païs …" (vol 1, 1608)

• Daniello Bartoli, "Dell'istoria della Compagnia di Gesu` l'Asia" (pt. 1 book 3, 1820).