NCAA have a problem with this?

If it is a family member who is putting your son up, there is going to be no problem. It's the kids that are taking money, cars, etc. underneath the table that will jeopardize a career; and even those kids don't get in trouble (very often.)

Many programs require all their players to live on campus, at least in the first year or two.

From my experience, if you live with a family member, you are allowed to live off-campus to save costs. It would be unfair to make a kid live on-campus without having a full-ride when they could live at home (or with a relative) for free.

It varies from college to college --- coach to coach. No one can give you a definite answer at this time. I wouldn't involve the NCAA. When the time gets closer call the coaching staff and ask if there is a problem living off campus. If there's no problem living off campus then ask the coach about the arrangements with the cousin. If he's OK with it then go for it. Another thing to consider ---- your son may have a different or additional options when the college selection time draws near.

My son's college allowed players to live wherever they wanted to live --- on campus, off campus, house, apt. etc. He always lived off campus and since he had no credit history I made the rent/lease arrangements and no one knew what the payments were except me and the renter. Some parents of players would buy houses or condos, let their sons (and others) live in the condos and the parents would have a place to stay when they visited. They would later sell the condo after he finished college and according to them, made money in the transaction.
Fungo

If the coach had no part in arranging the living arrangement and the college allows a freshman to live off campus there is absolutely no problem.
The coach cannot and din't assist a player in finding accomodations and so I am not sure what propmted the question.
That not only aplies to the coach but any friend of the college.

I dont see any NCAA issues here.

The only thing would be missing out on the college experience by living "at home" instead of on campus. IMO, students should experience dorm life at least one year.

The baseball player has a hectic schedule, being close to campus is a plus with their long days and many schools require tutoring sessions in the evening for freshman.