Jenny's would be a type of log of her goons (so similar to cult woman), because she logs her goons daily, so ig it would tell her what they're up to and if they die

Henry would be a medical log of some kind, ig he only sees when someone is injured on his

Josue would be a sketchbook sort of thing, he's kinda like Arthur in that he doodles things he sees so he's similar to the kid's diary

Mouse would be about scores, he logs things that look like easy targets for money, so ig if a train is nearby, his log tells him if its worth robbing or not, or if a rich traveler is passing by, etc etc. It also keeps track of the money they'd get from it since I imagine he keeps track of the gang's financials (sort of a log similar the the one in the VDL camp)