We want to go to Mexico on vacation. My cousin is a felon.
Would he be able to go?

He has to ask his parole officer, or office, if he is no longer on parole.
Some rights depend on the crime, others on the state laws you are in.

Same as Canada, Mexico is a foreign country to US citizens. No matter what the crime, trying to cross into Canada, they are not allowed entry. He will not be allowed, his passport will be denied.

tickle - it depends. Some felons can. My answer stands.

While often a visa is not required, it may be worth getting one or trying to, so you will know for sure. Often felons are denied entrance.