(Source: judgementpavilion.tumblr.com)

Deities that have been canonically approved:
Zeus (Rare) – God of honor, justice, lightning, and the skies
Poseidon (Rare) – God of earthquakes, horses, hurricanes, oceans, seas, and storms
Hades (Rare) – God of the underworld and wealth
Demeter – Goddess of the harvest and agriculture
Hermes – God of roads, speed, messengers, commerce, travel, thieves, merchants, athletes, and mail deliverers
Apollo – God of the sun, light, healing, music, poetry, archery, reason and prophecy
Ares – God of war
Aphrodite – Goddess of beauty, love, lust, desire, sexuality, and pleasure
Athena – Goddess of wisdom, handicrafts, useful arts, and battle strategy
Hephaestus – God of forges, fire, technology, craftsmen, sculptors, volcanoes, and blacksmiths
Dionysus – God of grape-harvest, wine, madness, parties, ecstasy and theatre
Hypnos – God of sleep
Iris – Goddess of rainbows
Hecate – Goddess of magic, sorcery, witchcraft, crossroads, trivial knowledge, and necromancy
Tyche – Goddess of luck and chanse
Nemesis – Goddess of balance, justice, retribution, and vengeance
Nike – Goddess of victory
Hebe – Goddess of youth
Asclepius – God of medicine
Kymopoleia – Goddess of violent sea storms (At least we can assume? Since Jason promised a cabin for her kids)
Notus – God of south wind and summer (Hinted by Zethes in the Lost Hero. He first mistook Leo as a demigod of Notus)

Deities that have history of demigods:
Iapetus – Titan of mortality
Helios – Titan of the sun (But remember that Apollo says he’s ‘faded’ in the Titan’s Curse. So unless you want to go with the idea that he’s returned with the rest of the titans stirring…)
Selene – Titaness of the moon (Ditto to Helios)
Eos – Titaness of the dawn
Aeolus – Master of the winds (Possibly)
Boreas – God of the north wind and winter

Deities that have no history of demigods, but have history of interacting with mortals:
Eros – God of love and desire
Thanatos – God of peaceful death
Prometheus – Titan of forethought and crafty counsel
Morpheus – God of dreams
Eris – Goddess of strife and discord
Phobos – God of fear
Deimos – God of terror
Aeolus – Master of the winds (For sure)
Zephyros – God of the west wind and spring
Macaria – Goddess of blessed death
Melinoe – Goddess of ghosts
Eros - God desire, affection, and erotic love

Deities that have no history of demigods or interactions with mortals:
Ananke – Protogenoi of inevitability, compulsion and necessity
Chronus – Protogenoi of time (Not to be confused with Kronos the titan)
Pontus – Protogenoi of the sea (He’s also been asleep in canon)
Thalassa – Protogenoi of the sea, consort to Pontus
Tartarus – Protogenoi of the deepest pit of the underworld (Also no physical form, but Rick gave him one)
Nyx – Protogenoi of the night
Hemera – Protogenoi of the day
Hyperion – Titan of light
Mnemosyne – Titaness of memory
Oceanus – Titan of the ‘all-circling river’
Phoebe – Titaness of intellect and oracle of Delphi (before giving it to Apollo on his birthday)
Tethys – Titaness of fresh-water
Theia – Titaness of shining light
Asteria – Titaness of nocturnal oracles, necromancy and falling stars
Astraeus – Titan of dusk
Lelantos – Titan of hunting/stalking prey
Persephone – Goddess of springtime and flowers
Khione – Goddess of snow (She also makes it clear in the Lost Hero that she doesn’t like mortals)
Phorcys – Protogenoi of the hidden dangers of the deep
Psyche – Goddess of the soul
Brizo – Goddess of sailors, fisherman and prophetic dreams
Alala – Goddess of the war cry
Euros – God of the east winds and autumn

Deities that are absolutely off limits:
Hera –Goddess of marriage (Faithful to Zeus)
Amphitrite – Goddess of fish, seals and the sea (Faithful to Poseidon)
Artemis – Virgin goddess of the hunt and moon
Hestia – Virgin goddess of the hearth
Britomartis – Virgin goddess of traps
Aura – Virgin goddess of the breeze
Hygeia – Virgin goddess of good health
Astraea – Virgin goddess of justice
Electryone – Virgin goddess of the morning
Aether – Protogenoi of the upper air and heaven – the substanceof light (No solid form)
Chaos – Protogenoi of the void and lower air – the substance of nothing (No solid form)
Uranus – Protogenoi of the sky (His physical form was destroyed)
Kronos – Titan of time (He was stuck in the underworld! Unless he got around when he was inside Luke…)
Rhea – Titaness of fertility and motherhood
Atlas (He’s busy holding up the sky)
Metis – Titan of wisdom (Zeus ate her)
Keto – Goddess of sea monsters (She only births monsters)
Pan – God of the wild (He’s a satyr. And he’s been 90% dead)
Harmonia – Goddess of harmony and concord (Turned into a snake)

Deities that can be debated:
The muses – Clio, Urania, Melpomene, Thalia, Terpsichore, Calliope, Erato, Polyhymnia, and Euterpe (Some myths say they were virgins. Some myths say Apollo banged them all. #Playah)
Gaea – Protogenoi of the earth (It’s canon that she’s been sleeping for forever. We really want to put her on the off limits list…) (Some myths say she’s the mother of the first kings, several human tribes, and Tityas. But it’s all questionable and vague)
Triton – Messenger god of the sea (It’s possible he has at least interacted with mortals, or if this was a different Triton entirely. Remember he’s a merman, though, so…)

Notes