The correct option is D has
It is to be kept in mind that Either, Neither, Each, Everyone, Many a, must be followed by a singular verb.
'Either book in the series' means each individual book. So, we are referring to a singular noun. By the general convention, a singular noun takes a singular verb.
Hence, option C 'has' is correct and option B 'have' is wrong.
Options A and Option D are irrelevant to the context.