11/17 is the last day you can check out a book from the Library. You can check out books on 12/22, but only have until 12/24 to finish reading it, so it is inadvisable to wait till this day. There are days where you get a seat the subway for your morning commute, allowing you to read a book as a free action. Try to avoid spending actual time reading a book and utilize the following days to obtain this trophy:
4/20, 4/25, 4/30, 5/21, 5/24, 5/30, 6/3, 6/15, 6/23, 7/1, 7/4, 7/8, 9/24, 9/28, 10/6, 11/2, 11/5, 11/10, 11/14, 11/17
Additionally, if you rank up the Temperance Confidant, you will unlock the ability to Slack Off during class, where you can make progress on these books without dedicating time.
If you are aiming to be time efficient, try to unlock Speed Reading as soon as possible, as this will allow you to read at twice the pace. You can unlock Speed Reading by completeing the books Master Swordsman, Call Me Chief, and Reckless Casanova in that order. As soon as Jinbocho is unlocked, go there to get the first book of the chain.
Do not read any of the books that unlock travel locations; with the exception of a few, you can unlock the travel locations through other means, such as story or Confidant ranks. Once you have discovered a travel location, you can then read the book for "free" since you already know the location.
For the books sold at Shinjuku, they will not be made available for purchase until you do the action associated with the topic. For example, you will not be able to purchase Essence of Fishing until you have at least gone fishing once.
All credit to xNinjaOfChaosx