My suggestions are in bold
Gaia - Arceus because Gaia created the universe
Groudon or Regigigas if you're only considering Legendaries, Torterra also can work
Uranus - Palkia because Uranus is the god of the sky and space
Rayquaza
Cronus - Dialga because Cronus is the god of time
Zeus - Zapdos because Zeus is a thunder god. It doesn't hurt that they both start with Z.
Thundurus
Hades - Giratina because Hades is the god of the underworld
Yveltal could work too because it's associated with death
Poseidon - Kyogre because Poseidon is the god of the ocean
Oceanus fits more with Kyogre I feel. I like Kingdra for Poseidon
Hera - not sure, this is a tough one. Hera is Zeus's wife, the god of marriage, and very jealous. We can't think of a good Pokemon to match that.
You're right, this one is tough but, if Zeus is Thundurus
than Hera could be Tornadus. Besides Tornadus Therian Forme is a bird which although is not a peacock could represent Hera
Athena - Noctowl because Athena is the god of wisdom and she has an owl. Only problem is that Noctowl is not Legendary.
Uxie is the knowledge pokemon
Apollo - Could be Meloetta because Apollo is the god of medicine, art, and music (among other things) and Meloetta's songs can heal people. Slight problem is that Meloetta is female. Moltres is another option because it's a Fire type that makes beautiful sounds and Apollo is also a sun god.
It's a bit of a stretch but, Mesprit. Mesprit is the emotions pokemon. Music, poetry, and art all play on the emotions
Diana - Xerneas because Diana is a protector of the forest and deer are her animals. Could also be Lunalea because she's the moon god.
Diana is Roman. Artemis is her Greek equivalent.
Hermes - Lugia because Hermes is the messenger god and Lugia is the messenger Pokemon
Latios
Hephaestus - Heatran or Volcanion because they're Fire/Steel types and Hephaestus is the god of volcanos and metalworking
Helios - Solgaleo because Helios is the sun god. Apollo is also a sun god but Helios is the main deity associated with the sun.
Hercules - Machamp because it's strong and it's a pseudo-Legendary and Hercules is a demigod, not a full god
Based on appearance than yes but, if your definition for the gods is a
Legendary than a pseudo-legendary mon would fit better
Hydra - Hydreigon because it's directly based on Hydra
Gyarados
Sphinx - Null because it's got a lion's body and its identity is a mystery
Luxray: It may have also been inspired by the mythical sphinx, as its short face, human-like ears, and lion-like appearance are similar.
Medusa - Yveltal because they both turn things to stone by looking at them
Serperior