Ok, That did it, and it worked. It is a bit of a pain, but it works if you care about the cover art. In detail, here is what I did. I went to the folder on my computer where all the books are stored. It is in the home folder (a little house on my Mac). Then, I opened the "Music" file. Inside that, I opened "iTunes Media" and then "books". In that folder are all the books I have ever downloaded, sorted by author. They get put in there automatically by iTunes, I guess, I did not set up the folder.
To be safe (since iTunes put them there, it could probably remove it, as well), I moved the files with the books with no cover art to the desktop. Then, I opened iTunes and deleted the books from the library. I then removed the same books from the iPad library.
Going back to iTunes, I added the books on the desktop to the iTunes library. They came with the cover art I had previously, so I did not have to get it from Google again. Then, I synched my iPad, and the books, with cover art, appeared again in all their glory. By the way, after adding the books, the ones I had removed from the iTunes media file we placed back in there again by iTunes.
Thank you to all who helped out with this rather annoying issue.