The equal protections clause, as other people are not required to sell through an independent middle-man. Perhaps the due process clause as well, depending on how the statute is written and enforced.
I don't believe the equal protection clause would be applicable. All residents of New Jersey are subject to the same standards, and the state would be able to articulate a rational basis for the restriction (ensuring consumer access to repair and warranty service, for example). Same with the due process clause, the state merely needs a rational basis, or a "legitimate governmental interest", which is reasonably trivial for consumer protection legislation.
State commerce seems like a much more reasonable limitation on states rights as dealerships are in effect a tax on imports from another state. Presumably, consumer protection rules like forcing any place that sells cars to also repair them, but states can't for example prohibit someone buying a car in another state.