Ok a lot of these are just vibes so please feel free to disagree with me in replies or whatever lol. Also disclaimer that a lot of these are going to be Apollo for....obvious reasons....and also that really they could all be coded as children of Apollo because singers who sing performers who perform etc.

Seungcheol-Instinctive answer is Nike, because you know. Competitive guy, goddess of victory....I can also see Zeus or Poseidon for him, something commanding/dramatic yk

Jeonghan-Athena or Hermes but I'm leaning Hermes. I think Hermes fits better with Jeonghan being like..."crafty"? Like obviously he's very smart but I would categorize it more as being intuitive/good with people rather than purely book smarts, which COULD be Athena as well but idk I'm thinking about in the pjo books how kids of Hermes always have this kind of mischievous/sly look in their eyes

Joshua-Aphrodite or Athena, the former is just vibes and the latter because Joshua strikes me as a very crafty person...the bracelets, the pottery (? that was a thing right) etc so. Goddess and patron of artisans/handicrafts.

Jun-Apollo. Look at BETS Jun performing Wave and tell me that's not a son of the sun god.

Hoshi-Apollo! I could see a lot of other options for him but Apollo makes the most sense to me

Wonwoo-Athena all the waaay. I don't even think I need to explain this one really.

Woozi-This is a son of Apollo. Maybe he even IS Apollo. Literally god of music, Seungcheol said it himself end of discussion.

DK-Ok so the obvious answer is Apollo but I'm actually leaning Dionysus because in addition to being the god of wine Dionysus is the god of theater and I think in a group of theater kids DK is perhaps the most theater kid of all!

Mingyu-Mingyu has such massive main character energy that I feel like being a son of Zeus would be appropriate lol. It's funny because in terms of personality/hobbies I feel like Mingyu is kind of suited to being like, idk a son of Hera or Hestia or something but that is obviously...not possible at least in the versions of the myths told by pjo sooooo maybe Demeter? I think Mingyu is obviously very athletic etc but I think in terms of personality he's quite nurturing so....

Minghao-I'm thinking Athena! I don't think I'm enough of a Minghao Scholar (TM) to explain this one fully but I think beyond the whole visual art thing (analogue for weaving/tapestries in my head) there's also like...this element of temperament? Or like, Minghao's approach to life that feels very Athena, or more accurately feels very PJO Annabeth.

Seungkwan-I have a hard time picturing Seungkwan not performing in some way? so again easy answer is Apollo, but I can also see Athena for him for some reason

Vernon-Ok this one gave me a lot of trouble....Apollo is as always the easy answer but for some reason I want to say Hypnos or Morpheus??

Dino-APOLLO. Dancer who dances!!!! Consummate performer!!! I could also see Dionysus purely on the basis of yk. #SendDinoToCannes. But I'm saying Apollo.

(This was way harder than I thought djl;aksl;dsa)