It's the Blow-me-Down Nature Trail on the South Shore of the Bay of Islands (West Coast).
I listened to the clip but it didn't sound quite right. I did, however, find this clip of a common nighthawk on YouTube and at around 19 seconds he dives and makes a sound similar to what I heard.
http://www.youtube.com/watch?v=7kJXiFPnlIE
I'm thinking that you're both right. Does any other birds come to mind so that I can look into it?