Is it permissible for me, as the administrator of a restaurant's Facebook page, to accept and publish photos of immodestly dressed female customers uploaded by the restaurant owner, and would I be sinful for doing so?

A Muslim is not permitted to accept or condone reprehensible acts, and this includes posting pictures of unveiled women on the internet. If you are able to prevent this person, then you are obliged to do so. Otherwise, advise him with wisdom and a good admonition, as long as no significant harm befalls you. Your silence, while being able to object, is considered an acceptance of the reprehensible act, which is not permissible.