Zeus:
Weather Control is the most obvious one. It has to be something with lighting bolts.
Hera: This is more difficult. Unlike the others, she doesn't have a domain that easily translates into a power. Based on some of the myths, I'd say a power that gives you influence over others. Maybe
Enhanced Persuasion.
Poseidon: The easy thing to do here would be
Hydrokinesis or
Water Empathy. However, that doesn't really cover all of what he can do. Perhaps a form of hydrokinesis that only works on salt water?
Ocean Manipulation.
Dionysus: An
Empathic Aura that produces escatic or frenzied feelings as desired?
Apollo: Ehh... He does have alot of domains, doesn't he? I have no idea.
Artemis: This is actually easier. I would just say
Superhuman Agility/Dexterity. Enhanced physical parameters tie in with her hunting.
Hermes:
Superhuman Speed. What else?
Athena:
Superhuman Sapience or
Superhuman Intellect. Both are fitting for different reasons.
Ares:
Empatheticaly Enhanced Superhuman Strength. Anger only makes him stronger.
Aphrodite:
Subliminal Sexuality or
Pheromone Production . That fits.
Hephaestus:
Godlike Craftsmanship? A slightly more generic one would be
Superhuman IngenuityDemeter:
Plant Control/Growth perhaps emphatically based.
“She'd become a governess. It was one of the few jobs a known lady could do. And she'd taken to it well. She'd sworn that if she did indeed ever find herself dancing on rooftops with chimney sweeps she'd beat herself to death with her own umbrella.”
― Hogfather