There are only a few firms that I know about who specialize in conversions.
In particular I'm thinking of Javlyn Automation of New York, who specialize in PLC-3 conversions. Control Technology Inc. specializes in support and conversion of legacy TI 500 series controllers.
In most cases, you'll find an integrator or engineering company in a particular industry who sells and supports a modern platform and is skilled with migrating the older platform.
Answers will vary widely depending on geographic location: I'm not sure Javlyn would be interested in working in India.
If you can be a little more specific about the controller brands and technologies you are interested in, I'm sure you can get better advice.