Well, since AMCAS doesn't even submit your info to the schools until the last week of June or so, the secondaries don't come out till then. The ones I got in late June last year were (in chronological order):
-U Chicago
-Columbia
-U Michigan
-Ohio State
Edit: Also, there are some schools that open their secondary websites earlier than that but don't formally send out an "invitation" email for you to fill it out until later. However, I've heard that some of them frown upon people that jump the gun and log into the application ahead of time so I would wait for the invites before you do so.