Hi, carpetmojo. Is your e-library run by Overdrive? Perhaps you are using the wrong file format? In the US many audiobooks are WMA. You need to download audiobooks that are MP3 format. WMA won't work with the Sony ereaders.
Many libraries in the US and UK use Overdrive as their source for ebooks and audiobooks. I use the Overdrive Media Console software to download audiobooks. It places them on my hard-drive in the folder "Documents/My Media/MP3 Downloads". The MP3 audiobooks do not have DRM; it is the honor system for you to delete them when they expire. Connect your 650 to your computer via USB. Then drag-and-drop the MP3 files into the folder database/media/audio on your ereader.