Where can I borrow older books that the Library doesn't carry anymore?

Ask a reference librarian to get them through interlibrary loan (from another library). If the book has to be brought in from another state, there might be a small fee, but the librarian will tell you that upfront. There is a world-wide database called WorldCat that gives good info on where books are located. Or, you should be able to use your card at other nearby libraries, if the book you want is in your area and you don't mind driving to pick it up.