Have you checked out this link yet?
https://wiki.mobileread.com/wiki/EBook_Lending_Libraries
Libraries usually offer two formats:
1) adobe digital editions (pdf)
2) mobi (prc)
*A third format is growing in popularity with libraries: epub
Sony reads the ADE pdf format.
Cybook reads the MOBI prc format.
I'm not sure but Bebook may also read the drm mobi at this point?
I know some Kindle people were using a special program to
be able to convert the mobi books from library to a Kindle format
but not sure if that is still available (due to Amazon changes/policies/etc).