Many Landlords often say no pets on their listings and they are with in their right to do so. However, you have found the perfect rental property and it says no pets how can you over come this obstacle? Firstly it does pay to ask, if the property has been vacant for a while the landlord may make a decision to rent to some one with a pet. Offer, if possible a reference from a previous landlord regarding the pet, that could ease any worry over any pet issues. Perhaps offer a little more rent a month to compensate for any potential extra cleaning when you move out.
In New Jersey a landlord cannot ask for an extra pet deposit. Security deposit cannot be more that 1.5 months rent. You could offer to put extra money in escrow but the landlord cannot demand it.