I'm making my way through mystery, thriller, and detective fiction right now in anticipation of writing something myself, and I decided to look at Greeley because he's been a successful crossover writer. He's a Roman Catholic priest, college professor, and writer, and his novels usually combine all of his vocations somehow.
An Occasion of Sin is a mystery, of a sort. An R.C. Cardinal has been killed in Central America, and the laity are moving for his beatification and eventual canonization as a saint. But the Vatican wants to keep control and isn't so sure about whether the guy is fit to be a saint or not. Greely follows the investigating priest (in what used to be called the Devil's Advocate role) as he tries to find out the truth about this man who would be a saint.
While it's an interesting book with multiple narrators, it falls flat in some key places, particularly in terms of dialogue, which often seems forced. It's a good read if you want to learn something about the 20th century process of beatification in the Roman Catholic tradition, however.
UPDATE: I finished An Occasion of Sin and found it harder to put down as I neared the end. Some of the revelations in the latter part of the book were fairly predictable, but the book gained momentum as the narrative came to a close, and the lead character continued to be engaging enough to follow around.