A friend recommends Rohini Lokhande at the Law College Tennis Courts. Specifically for young children (under 10).

Deccan Gymkhana - The biggest Tennis facility in Pune with 11 Courts, also has probably the best coaching setup. From entry level coaching to professionals (the top coach at Deccan Gymkhana is former Indian National Champion - Nandan Bal). Many different instructors coach here - someone else can add those details here.

You can also enquire in the Deccan Gymkhana Club-House about further details (open 8-11am and 4:30-7:30pm, Mon-Sat).

Gaurav Natekar, Arjuna Awardee, Davis Cupper, and Asian Games gold medallist and his wife Arati Ponnappa, Federation Cupper, 7-times National Champ live in Pune, and also do coaching, but I don't have exact details. But their contact info is here - and you should be able to get info from there.

Hi, Shrinivas Rao is a good coach especially for beginners. You can get his contact details at http://engageyourkids.com/