The deductible property tax for your federal tax return as an itemized deduction is only on property that you own. The property taxes paid on rental property is deductible by the owner of the property for federal tax purposes, not the tenant or renter.
For additional information, please refer to the following link:
What you can do in NJ is claim your rent on your state return.
There is not a rent deduction or credit on your Federal return. If your state has anything for renters you will be prompted to enter your rent info when you complete your state return. As far as I know, the states that have anything for rent are Arizona, California, Connecticut, Hawaii, Indiana, Iowa, Maine, Maryland, Massachusetts, Michigan, Minnesota, Missouri, New Jersey, New York, Rhode Island, Vermont, Washington DC, and Wisconsin.