The reality of looking for yearly rentals is that realtor listings are the least likely source of such properties in the near-shore area around Ocean City NJ. Property owners know that supply and demand favors them, so they can advertise on their own, take their pick of prospective tenants, and avoid paying commission. Some owners don't want to do this and use a realtor, but if you look in the local newspapers you will likely see more yearly rentals advertised than you will on trulia, realtor.com or other websites. You can also find yearly rentals advertised on Craigslist but be very wary of yearly rentals listed in shore towns. Unscrupulous individuals have frequently copied photos and text from online sale listings and posted them for rent at prices well below market, usually with a back story about the owner's unavailability to show the property.
I suggest you google the Gazette newspaper for different towns in the area (Ocean City, Somers Point, Upper Township, Egg Harbor Township) and look at their online classifieds, as well as trying the Press of Altantic City. This close to summer, there may be some mainland availability as the school year winds down. The beach towns will be very tough especially with the 2BR/2BA requirement along with pet friendly.
Good luck in your search.