The credit for taxes paid to another state doesn't really work that way.
You would need to do the non-resident state return FIRST, then any tax liability to that state would trigger a credit for the resident state.
Since you don't really owe New York any tax, New Jersey would not like the idea they they are giving you a credit for something you shouldn't be paying.
Depending on the program you are using, if using Online you might be able to do the New York return, print and mail it, (so not charged) then do the New Jersey return and e-file that.
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