Hmm, no pirate would own a frigate, you probably wouldn't even be able to buy one. Unless you capture a frigate (which is highly unlikely) the best ship you can hope for is a trading galleon or a brig.
The sloop is underestimated, there is a great deal a skilled captain can do with a quick sloop. If you want to buy another ship, Tortuga is full of them, or you can try to capture one.