Hi, I'm not a lawyer. I used to rent though so I got familiarized with laws before that. I'm also not familiar with NJ law (maybe you'll get other replies as well).
What your association can do is written down in your bylaws and rules and regulations. No one can answer questions regarding what they can do without reading your docs because it varies from association to association. If I were you, I'd go and review my bylaws and rules and regulations and see what restrictions there are. In my association there is a pet weight limit on dogs for example which applies to both owners and renters.
I would also contact association and tell them that I can't just ask the guy to remove the dog as this is in his lease (assuming it is in his lease). Asking someone to remove a dog is in effect more likely than not asking them to leave. If he has a fixed term lease (like my association requires), your only course of action is to try to evict him. If the dog has not actually bitten anyone, you may very well loose an eviction case. I'd tell them that I'd be more than happy to work on removing the dog but I'm not sure what I can do about it legally. Maybe they can talk to the association lawyer about it on your behalf.
But in general, I used to just not allow dogs after a tenant who ruined the carpet with her chihuahua.
I hope this helps.