P_Reysner is correct, though whether a corporation can be defamed is dependent upon local jurisdictional law. Corporations have filed suits for defamation in several states, and California does allow corporations bring defamation actions. See Sources below.
Defamation requires showing harm to reputation for some individual, or for a corporation if the corporation is named as the party who committed certain acts.
Brown is talking about what some people did 2000 years ago, and what some fictional people have done since then. He has formally disclaimed, saying that he's not talking about any current living individual. Nor, from what I have read, has he made any claims that the actual Catholic Church as a whole has actually done certain things.
Since there is no possibility of reputational harm to any single living individual's reputation, no person has standing. Also, since he has never claimed the real Catholic Church has actually done things (since he calls it a work of fiction) there is no way to show reputation harm to the organization.
It's not defamation to say something that someone else doesn't agree with. And the church's main problem is that they consider his work heresy, even though it's fiction. But heresy is not (Thank the Gods) against mundane law.
Also, given that the Catholic Church is a public (famous) entity, consitutional protections would kick in. This would be the same for any large church, corporation or government agency, since all would count as public/famous entities.
Thus for the Catholic Church to succeed at a defamation claim as plaintiffs, they would have to prove (1) that the statements Brown made were _objectively_ false, (2) that Brown knew the statements were objectively false, and (3) that Brown intended people to believe the statements were true. Number 2 is easy: he claim's it is a work of fiction. But that makes proving #3 almost impossible.
And good luck proving #1 as objectively false in a court of law, since that would require a witness to the events or the original author of a document that was recognized by the court as being literally valid under rules of evidence.