I think the story book might be located in a special vendor's shop. Sometimes, these unique items are sold by specific NPCs. Or, it could be a reward for completing a challenging side quest.
One idea could be a rengoku fanfic where he trains a new group of young slayers. It could focus on his unique teaching methods and how he instills his values in them.
Tanjiro would be a great character to pair with rengoku. Their different personalities could create an interesting interaction. Tanjiro's kind - hearted nature and rengoku's fiery determination could lead to some great storylines.
One great 'Slayers fanfiction' story is 'The Adventure Beyond the Known'. It takes the characters on a new quest filled with unique magical creatures. The author does a great job of capturing the essence of the original series.
One popular theme is alternate universes. Fans like to imagine what would happen if the characters were in different settings, like a steampunk world or a post - apocalyptic one.