“On our school library web site we post the titles and authors of books that have won our school district’s Favorite Picture Book Award (both current and past winners are listed). Would it be legal to copy and paste a picture of the book’s cover to accompany such a posting?”
Since you are using the pictures for educational purposes you should be fine. It would get tricky if you wanted to somehow use the website to generate money. Drop us a line before you get to that bridge.