I'm unsure about how you may add the information to Sony's own site as Sony don't seem to contribute at all from what I've seen on these forums.

Perhaps you'd consider making a post on www.mobileread.com? There is already a thread on there with a list of UK libraries.

Would you mind saying what your joining criteria are? Do you have to be Wirral resident? And perhaps how many books you currently have in your collection?

Thanks

Wirral Libraries does show up in the North West section when 'Browsing for Libraries' on my Sony eReader,

a previous poster has mentioned there is a thread on MobileRead where you can add information on

Wirral Libraries.