Can i buy a home in north carolina if i live in nj?

Yes you can but you would have to get an investment loan that differs from a normal mortgage loan and usually requires a higher down payment and more expensive insurance. A better suggestion would be to try to co-sign a loan with your son and have your son be the owner occupant. It does not matter which state you originate the loan, but only your lender could specify how much down payment would be required. I do suggest you look into the FHA Kiddie Condo program as it seems very applicable to your situation.