Is coffee native to India?

Coffee was first grown in South India during seventeenth century in Karnataka

No. Legend has it that during 1650s, a Moslem named Baba Budan went on a hajj (holy pilgrimage) to Mecca. He brought back seven beans with him and sowed them at Chikmagalgur hills in Karnataka where they thrive to this date. During 1690s, a Dutch owned 'East India Trading Company' planted coffee beans on the island of Java (Indonesia) and later in Kerala and Karnataka. The coffee from Java gave rise to the expression 'cup of Java', and coffee from Chikmagalgur to 'cup of ole Chick'.