Obtaining paid work in India is harder than you might expect, and local wages rarely make this cost effective for travellers. Business trips are easy, but working for an Indian company requires visa sponsorship from an Indian employer and finding a job before you travel. Although not strictly legal, casual opportunities exist at some tourist resorts teaching adventure sports and holistic therapies. However, this may deprive locals of much needed employment.
There may be opportunities with international package holiday companies for tour reps in Goa and Kerala (though you normally need to complete seasons in Europe to qualify), and opportunities for drivers and guides with the big overland tour companies.
If you’re a Bollywood fan there may be opportunities for working as an extra in Mumbai. Film crews also visit traveller hotels in Chennai looking for extras for the day.