The only classes that can create spellbooks are arcane, and they can only learn arcane spells, so they cannot create a divine spellbook. As a result, there is no such thing as a divine spellbook, and officially, a divine spellcaster with mnemonic vestment is stuck using scrolls. This isn’t a huge hardship, but it is one.

Personally, I let divine spellcasters produce “prayerbooks” for this purpose if they like. I made the same ruling for a warpriest with the arcane bond ability, for example. And I also use D&D 3.5e content, which includes the archivist class from Heroes of Horror—which explicitly and officially keeps a prayerbook, being a kind of divine wizard. But the official rules wouldn’t let you do that. And it’s hard to argue with someone who wants to limit the effectiveness of mnemonic vestment, seeing as it is extremely powerful.

The only classes that can create spellbooks are arcane, and they can only learn arcane spells, so they cannot create a divine spellbook. As a result, there is no such thing as a divine spellbook, and officially, a divine spellcaster with mnemonic vestment is stuck using scrolls. This isn’t a huge hardship, but it is one. Turned out to be incorrect, see pi4t’s answer.

Personally, I let divine spellcasters produce “prayerbooks” for this purpose if they like. I made the same ruling for a warpriest with the arcane bond ability, for example. And I also use D&D 3.5e content, which includes the archivist class from Heroes of Horror—which explicitly and officially keeps a prayerbook, being a kind of divine wizard. But the official rules wouldn’t let you do that. And it’s hard to argue with someone who wants to limit the effectiveness of mnemonic vestment, seeing as it is extremely powerful.