The lay leadership at many Catholic universities has resulted in some of them becoming really secular universities (ie, Georgetown). So, a careful decison should be made here. If that's the direction, I like Mike Simons, who is the dean of the law school. He's young, committed to SJU, and done a good job in a short time at the law school. He's a real legal wonk, though, so I don't know if he would be interested.
Regarding lay leadership:
Is lay leadership at Catholic universities really causing secularization? Can a devout layperson effectively run a Catholic University, still leading a school with a religious mission, but be a more effective administrator in process? Would a faithful layperson with a strong background in academic administration with the proper educational credentials be more qualified than a priest who is selected from a rapidly diminishing pool of ordained candidates?
There are 1.6 million Catholics in the Brooklyn Queens Diocese alone. There are about 300 active priests in the diocese, down from over 400 about a decade ago. The Vincentian Western province has about 140 priests, and I cannot find the number in the Eastern province. Its reasonable to maintain that along with an aging priestly propulation and rapidly declining number of new priests, there is also a much smaller number of priests qualified to run a university.
My son goes to Xavier HS in NYC, which is Jesuit, and one of the oldest high schools in NYC, dating back to around 1840. Their current president is a layperson, and in deed and word, there has been no decline in the religious or academic mission of the school, and certainly not in leadership. It could actually be argued that both traditions are on the rise at that school.