Yes you can.
The easiest way to do this is to give ALL your subscribers both books, but only mention one of the books in your signup form or squeeze page. Then say that the "extra" book is a "bonus".
You can make the headline on your download page say "Here's your free book (plus a bonus!)", and follow this up by saying "I've decided to give you another book free, as my way of saying thanks."
And then you just don't tell people which book is the one they requested, and which one is the bonus. Your subscribers will just assume the book they didn't sign up for is the bonus, and they'll love you even more for overdelivering!
You should also make sure that your confirmation email does not mention which book they have signed up for.
See "How to add or edit the ebook on your download page" for how to edit your download page so that subscribers can get two books.
And "How to change the ebook on your squeeze and signup forms" to see how to add another signup form and/or squeeze page to your site for your second book.
Note that we don't recommend that you run a separate newsletter list for each ebook, since this will very quickly get confusing.