Many universities have aircraft. (And not just for coaches or athletic directors... other Deans and Administrators use them too!)
Here are a few that I know of. Some are owned by the University, others by various University foundations or trustees. You can probably find more if you search the FAA registry by owner name:
University of Alabama: Citation 550 and MU2 (plus Mini 500 for their flight research program.)
Virginia Tech: Citation 560 and a Citation 550
University of Arkansas: King Air 200
University of Mississippi: Citation 500
University of Nebraska: King Air 200
Notre Dame: Citation 560
University of Virginia: Citation 550
University of Wyoming: Kingair 200