TD,
As you see there are a lot of options out there.
Since your cousin is a beginner, its probably best to get a plastic kit, one he or she can build easily and have the reward of a completed model. It should be low cost, and if messed up a bit on the first time, no worries.
It should also say "Pirate Ship" on the package - regardless of what is actually in the box. This adds to the fun. Pay no attention to the fact that the model is actually a French this or English that. They all have cannons and sails. Its all about the imagination.
The Lindberg kits are perfect - you can pick any of them up for little money, they all have pirates and skull anfd crossbones on the package and come with fun pirate flags for the model. It does not matter which one, they all build about the same. I strongly recommend them.
If your cousin wants to build in wood, which is more challenging, the Amati Pirate Schooner is a good one, since its based somewhat on a Barbados sloop, actually used by pirates from time to time, and is as simple as wood ship kits come. But its still challenging, will take longer to build and require more skills, like planking curved surfaces, etc.
I would not recommend the Artitec Dutch jacht, as its more advanced and requires extra skills. Its a gorgeous model, I'm building one myself, but in resin and etched brass more like a MIG forum thing than a entry level impulse pirate ship model.
Bottom line - go with a Lindberg pirate ship kit.
Hope this helps, Jim