I want to say ah-QWIN-na, because it makes the most sense to me in English, but I know it's not an English word and I have heard ah-KEE-na somewhere, so I called Aquinnah, MA to find out how the locals say it. The library's message and the guy at the Town Hall definitely said ah-QWIN-na. Because of this, I think you don't need to worry about ah-QWIN-na being a valid pronunciation, but there are no guarantees that it's the only valid pronunciation, if that matters to you.
I prefer the Aquinnah spelling.