Below are ministries which donate books for prisoners. I think they will accept donations of doctrinally sound books. You would have to contact them.
Christian Library International
Christian Library International is in need of new and used Bibles and Christian books to distribute to over 1,600 correctional facilities nationwide. Spanish language Bibles and books are also a huge need.
International Prison Ministry
IPM is a Christ-centered, Bible-based ministry directed primarily toward prisoners, their families, and those who minister to them.
Oliver receives hundreds of handwritten letters that bear a name and address of a Florida prison or jail—the largest prison system in the country—requesting novels, biographies, dictionaries, and reference books on subjects like math and engineering. Each week, Oliver organizes these letters that come to Open Books Bookstore, a nonprofit that launched the Prison Book Project in 2000, as a means to provide free books to inmates in the state.
Rescued not Arrested
Our mission is to reach the incarcerated Internationally and their loved ones with the good news of the Gospels, the Great Commission (Matthew 28:19-20). We have provided over 500,000 Bibles to inmates, Leper colonies and others internationally. We partner with over 500 prison Chaplains in the US alone to provide Bibles & Study Bibles free of charge each year. Locally, in Arizona jails and prisons we conduct Church services, re-entry support and one on one mentoring.
The Gideons International
The Prison Ministry Supply Store
PMI Center Ministry
The books you will find at The Prison Ministry Supply Store are offered on a donation basis. These books are helpful in assisting you in your evangelistic prison ministry outreach.
If you have any questions or need help finding a particular video, tract, book or any other Christian resource in any language of the world, please contact firstname.lastname@example.org