My character is Jack Aubrey. At the beginning he had got HMS Sophie. I aboarded Raa Frigate, then USS Constitution.
Anyway, you should open game, open Options, mod options and there're a few options and you can choose there COAS default or realistic. Change 'ship purchase' ( I think it was that option ).
If you change you, you'll probably find better ships and more models at shipyard. I think it depends from your experience too.
Anyway, I couldn't have found USS Constitution, so I sailed to Charlestone, went to shipyard and saved game there.
I loaded game at the same place about 40 times but I found USS Constitution. I bought it, later I found USS Constitution with better possibilites which was under French flag so I just change Union Jack to spanish flag and they surrendered.
So, change this option, sail to other island, go to shipyard, save game there ( don't talk to him about ships earlier ). Then just load the game and ask him about ships. There'll be different ships. Try it many times, you'll find it. I saw Black Pearl a few times but flying dutchman not.
The another way is ( as I wrote ) change lines in file of the game. You can choose there which ship you want to start with but it requires start the new game.
Btw.: I've never seen Black Pearl or Flying Dutchman which was sailing somewhere. I've seen Black Pearl at shipyard a few times so far. You can also talk to other captains which sometimes are in tavern. They'll probably have weak ships but if you have better level and you get better ship, they'll have better ships too. I saw one captain who had got Black Pearl when he joined to me and we made companion.
I had Black Pearl once but I don't know what cool you see in it. I like really well-made ships like Surprise, Raa Frigate, Unicorn, Nightmare ( love this ship but I've got better ) and Constitution.
Sorry for my English. Ask me if you don't understand something.