I haven't heard much of anything about Native Americans having an interest in seafaring. Did any Native American tribes attempt to navigate the oceans or build ships?
Native Americans of the Pacific Northwest such as the Makah and the Nootka definitely built whaling and sealing canoes.
It might help to more clearly define ship.
I'm not sure what OP is thinking, but I would imagine the thought is something with a hold and below decks quarters, primarily or exclusively sail powered, and too large to be sailed by just one person.
A follow up question. Did any Native Americans every participate in any sort of naval warfare?
The Haida people of BC built very large canoes and could travel the length of the modern day BC coast. You might like to look at the following documentary: http://www.cbc.ca/archives/categories/lifestyle/leisure/a-passion-for-paddling-canoeing-in-canada/the-haida-canoe-building-tradition.html