Most oceanfront rental owners want to get the benefit of summer rental income. There are a lot of condo complexes which do long-term winter rentals and monthly rentals in the shoulder months. So it is difficult to find any oceanfront year round rentals. I did research in MLS for active listings to determine which ones show rental to pet owners allowed. .
See list below-
Beachwalk Villas-Cherry Grove
Shores of Surfside II
Ocean Garden Villas
Cedar Ridge North Myrtle
Ocean Place 1
Bay Watch Phase 3 North Myrtle
You might try Craigslist to see if any of these show up with annual rentals available. Every condo complex will have rules regarding pets and individual owners have the right to deny pets EVEN if the complex accepts pets. One item to remember is that most towns do not allow pets on the beach in high season. The other consideration is whether your small dogs will be tolerant of the influx of people in high season in elevators, noise levels, activities, etc.
Please let me know if I may help you. Liz Smeltz, Real Living At The Beach, Realtor/Property Manager, 843-504-6888.
Wish you all the best in your quest.