If the stipend is taxable (not all stipends are), the stipend is taxable in both states. New York may tax you as a resident, and New Jersey as a nonresident, but NY will provide you a credit for the tax you pay to NJ on this income. In this case, you file a NJ nonresident return, and then a NY resident return. This way, the credit for taxes paid to NJ will transfer over to your NY return.
Another reason to prepare the NJ return first is to see if they actually tax the income. If you have a $0 tax liability in NJ, that would mean you don't have to file there, and you would only file a NY return in that case.
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