Had the same problem, turned out (I'm pretty sure, time will tell) to be calendar notifications. I have sound turned on for Calendar in Options -> Notification Center, which is fine because I want alerts and sounds to tell me about upcoming events. But in the Calendar page for notifications at the bottom, there are also settings for "Invitations", "Invitee responses" and "Shared calendar changes" which had sound turned on, but no banners, alerts or "show in notification center."
I have my work email account on my phone, so every meeting request I received, or every response I got to a meeting request I had sent was making the phone chirp. (The emails trigger it, but the setting was under "Calendar" since these are related to meeting on my calendar linked to my email.) Also, I have shared Google calendars with family members, and apparently whenever they changed anything in a calendar, I got a chirp as well. I've off sound for all of these, and we'll see if that makes the problem go away completely.
There really needs to be a better way in iOS to say "Show me everything that can make my phone make a sound" (right now, there are multiple incomplete ways only). Or how about if Siri could answer "Why did my phone just vibrate?"