I think your cousin is quite clearly lying or not telling the whole story.
When he applies, the Canadian visa officer will have access to all the documentation relative to his refusal to entry from the USA and the ban from the USA. That means he will likely get rejected unless he has a very strong case to enter Canada and very strong ties to India and lots of years have passed since he was 'deported' from the USA. That coupled with the fact that his immediate family will not remain in India and travel with him instead, means he will 99% get rejected.
Start him from asking for how many years he got a ban from the USA.
The best thing you can do right now is contacting a US lawyer dealing with such things so he can request all the files and documentation relative to your cousin's refusal/deportation, and start this whole process again.
Hire a good laywer and go from there. It's your only chance imo.