Sharon, it's harder to find rentals that allow pets, but it's not impossible. I can send you all of the listings that say they allow pets, but often others may allow them on a case by case basis. It would help to know how many and what kind(s) of pet you have (cat or dog), the breed, and how large (in pounds).
Email me the information, the number of bedrooms you're looking for, the price range, and any other things you'd like/not like.
Are you limited to Atlantic Highlands, or would you consider any of the neighboring towns? Do you need to be near the ferry, a train station, etc.? When do you want to move in?