The NC income is going to be zero until the passive loss carryover is used up. So there will not be any NC tax liability and thus no credit for taxes paid to another state on your NJ resident return. You do not need to complete the NC NOL schedule as the net rental income is included in the adjusted gross income already. When completing the NC Schedule PN, column B line 11 will be zero until the passive loss carryover is used up and your Schedule E shows a gain.
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