You can cover most of the parts of Kerala with less budget. As public transport is very cheap in all over kerala. You can go from one place to another by ferry as well which is much cheaper in Kerala.
I am not sure how many days or Where you planning to , but i can suggest you this.
If planning to travel to City.
Use Trains ( Esp City express) Quite economical and Fast too
Stay Hostels
Have street Foods. Planning on Trek Borrow a tent use public transport
The only expense would be permissions. and food ;)
Use public transport, if train then book general compartment.
Always have food from dhabhas( road side stalls) and opt for vegetarian.
Visit Kerala and places in Kerala like munnar and wayanad, most part of these places are accessible by local transport.
Reach Kochi by train and then take ferry to fort Kochi for Rs. 7. Buses to munnar only costs less than 150.
Use KSRTC buses for Kerala transport.
Instead of renting a tent, sleep in AC waiting ros in railway stations at cheap cost ( always remember to take platform ticket also).
Do couchsurfing for your accommodation, hitchhike to move around the places and use Public Transport where hitchhiking doesn't do the job and balance out of 2000 you can use for food.
Head To Pondicherry
Take bus from chennai to pondy which cost 300 both both sides
Then book a hostel which comes nearly 700-800
Still you have 1000rs
Consider 700 for you all meals
And with 300 hire a scooty and rome around pondicherry Enjoy. have a Happy Travelling To know more glimpses from Pondi check my photo blog here : https://www.tripoto.com/trip/a-much-needed-break-pondicherry-pondiphotos-5c8f6a3c849ce
2000 is may not be enough but if you use public transport and street food like idli,wada and stay in budget loudge that can be possible.
anyway enjoy your fullest..