I haven’t read the series but what I do know is that the children share the traits of their godly parents so I’m gonna give this a shot.
Bacon would probably be the son of Ares given his physical attributes. He doesn’t seek out fights but will protect those he loves at all cost. Although, as a side note, I know it doesn’t fit him at all, but would be hilarious if his parent was Aphrodite.
Kathryne’s parent would likely be Athena since she’s incredibly smart and very logical. Although, I’m not sure if he’s in PJO but Hypnos might also be a good fit since he’s associated with sleep and KitKat struggles with insomnia.