Nohea Kai in the Mauna Lani area may be a good place to look.
We rented a lovely, brand new 4 bdrm home w/ pool through Abita Rentals on Airbnb. (They are licensed, and Big Island has a pretty good sized inventory of legit Airbnb listings relative to the other islands because of all the new construction.)
The Mauna Lani area is a good location in general, many rentals there have access to the Mauna Lani Beach Club, and it’s a short walk to the Mauna Lani and Fairmont hotels. A car is necessary, though, to explore the island.