Every piece of advice I have read about applying to faculty positions emphasizes the importance of the cover letter. It should be brief, it should introduce all the critical pieces of your application, and it should be customized. If at all possible, mention any special requirements from the notice, or say something nice about the college or department; don't let them think this is just a form letter you're sending everywhere.
In theory, this is great advice. In practice, I could find nothing to say. I slaved over the cover letter template for over a week, from the time I learned one of my letter writers had gotten ahead of me until I couldn't stand it anymore. I struggled with the opening paragraph, which should summarize my qualifications and convince the reader that I will graduate in May. I sweated over the second paragraph, which was devoted to convincing faculty at liberal arts colleges that I knew what I was applying for. I condensed my teaching philosophy and teaching biography into one paragraph each, trying to convince committees to hire me without sounding fake or overdone. Then the same thing for my research philosophy (mentoring undergrads) and research statement. It was all the writing I did for a week.
I exhausted myself with the main points; I couldn't bring myself to customize. There wasn't anything less that didn't sound incredibly fake. What could I say about my ability to contribute to a college's "strategic plan"? The truth was that I'll do what I can if I'm hired, and I have nothing more to offer than that. Is it necessary to justify myself as a teacher of an unfamiliar subfield when they are so very tentative about what the course requirements may be? I'll teach what I'm asked to teach, and I'll do a good job of it, even if I'm learning what I'll be teaching only a few days ahead of the students.
In the end, I wound up with three template cover letters. One for a teaching fellowship, which will be adapted for any visiting professor positions I might apply for. Two are for the assistant professor positions, each with a slightly different focus on my research to cover the two main subfields I might apply for. Perhaps in the upcoming weeks, when the stress of drafting the first cover letter begins to fade, I will be able to come up with promising statements about how I am the best possible candidate for the job. At the moment, what they get is all I can do: This is why I am applying for this type of job, and why I think I'm qualified, and that will have to be enough.