Is there a way to get iBooks to display the generic cover for my PDFs?
You could convert them all to ePub using Calibre. Add the ePubs to iTunes and they should sync with iBooks. As not all PDFs are formatted the same, some will show the generic cover while some will show the first page when converted to ePub. You can change the cover art for each book individually in iTunes, by selecting the book > Right click > Get Info > Artwork.