Librarian’s or Librarians’

Before LBC was part of LISNEWS I wrote the name like this Librarians’ Book Club. I had at least two people email me and say that it should be Librarian’s Book Club. When LBC became part of LISNEWS I put the name as Librarian’s Book Club.
Someone posted a comment asking whether the name should be Librarians’ Book Club. I would like to come to a definitive answer. Can the grammar experts among the group weigh in? The name will either remain the same or be adjusted accordingly. If you have a source for your answer please cite it.