Under US copyright law, is it legal to download images of book covers from the Google Books API and display them on my website? The purpose pertains to obtaining product images for an online store that specializes in second-hand book sales.
Not necessarily, but also possibly.
Google Books may (or may not) have a license to distribute images of the book covers in question. This license would be between Google and the owner of the copyright of the book cover. Just because Google has a license to distribute the image of the book cover to you does not mean that you have a license to distribute the image of the book cover to your customers.
However, depending on jurisdiction, using the book cover to identify a book might also be legal under relevant fair use statutes.
It is also possible that the particular book cover is not protected by copyright. For example, a particular book cover might have entered public domain.
If this question is not a hypothetical, you should probably consult a lawyer.