"I read him a book."
Translation:Ben ona bir kitap okurum.
Kitap is the actual word. But you are right that "p" sometimes turns to "b" when it gets certain suffixes. For instance it becomes "kitabın" (of book). But there is no such affixes in here so its in its nominative form "kitap". If sentence were "I give him the book", it would be "Ben ona kitabı veririm"
I don't really know how to explain but it's like I like him: onu seviyorum. I hug him: ona sarılıyorum. I eat it: onu yiyorum. I touch it: ona dokunuyorum