So I called my cousin and he said basically officer put him in the interview room and asked him whether he has intentions of working here or not. He said few times "NO" to them but they made a pressure on him that you will be banned or put him behind the bars it doesn't say the truth and in that scary part he agreed that he came for work and signed his paperwork to deport him back and entry of refusal.
I agree with him anyone can get panic and do such thing so at least he gets home safe.
So now what option do we have?
You can still apply, but it's quite likely that he will be denied. You will have to explain the circumstances of his deportation from the US, and Canada will also have access to the files from the US so they can double check. Don't say stuff like "he was forced to sign" etc. It's best to be completely honest - making a mistake some years ago isn't necessarily a ban for life.
He'll have to show very strong ties to India to even stand a chance, and since you say his family is going to travel as well, it may be difficult.
Still, no harm in applying. The worst that will happen is that he will be denied (assuming you are completely honest in the application, of course, if you don't tell the truth you can be banned), and then he's no worse off than he is right now.