"Client" is exactly right. Librarians, like faculty members, have a body of knowledge and skills that they can bring to bear to assist those who seek their services, not as commodities, but as valuable to each individual, dependent on unique needs. Just as accountants, lawyers, etc., we, as professionals, offer services that users may seek, or not. But our users do not seek one-size-fits-all mass-produced products, as do "customers." So let's convince our colleagues and administrators that "client" is the appropriate word.
Personally I'm not into the word 'client,' but I love this person's definition of who our, er, clients are and why they make use of us.
Or to go in another direction, maybe we should start referring to our customers as 'library pets.'