In the greek world, gods are everywhere. Every idiom and vow, every legend and decision, include one of the gods as a reference. In such a theocratic society, clerics are important and powerful. At the same time, the true followers of the gods are few and sparse: most heroes of the greek myth were fighters, rogues and an occasional sorceress.
More than simply ch0ose a domain, a cleric in D&D Greek Campaign must choose a god, and then reflect what domain is appropriate to that god. Fortunately, most gods have many attributes and aspects, sometimes contradictory. For example, Athena is a god of pacific craftsmanship, but also of tactical war.
For this rulebook, we will take the convention that the clerics are ordained priest of the Olympian gods only: Zeus, Hera, Apollo, Artemis, Poseidon, Aphrodite, Hermes, Hephaistos, Dionysus and Demeter. This excludes Hades, Persephone and Hecate (the chtonic gods), and a myriad of lesser gods and ascended heroes as Asclepius and Heracles. The reason is that the Olympian are the only ones that are formally respected as a such, and that can have an organized cult like the Cleric class represent. The followers of those other gods could be better represented with other classes like Druid, Sorcerer or Bard. Unfortunately, some domains are a better match for the non-Olympian gods, like Death and Magic.
Core Archetypes
There is not a specific god of Knowledge in the Greek Pantheon, as required for the Knowledge domain. The Muses and their mother Mnemosine doesn’t have a priestly cult. Of the Olympians, the wise Athena or the mischievous Hermes are appropriate as patrons of a Knowledge cleric.
The god of Healing usually is considered Asclepius, but he is in fact an ascended demigod. Instead the Life Domain should be used for a priest of Apollo, Asclepius’ father. Alternatively, Hera, Aphrodite or Demeter could patronize a healing – based cleric.
The sun god in the greek pantheon is Helios, but Apollo also took the aspect of the god of the light. A cleric of the Light Domain should revere any of those gods.
Both Artemis and Demeter could the patrons of a Nature domain cleric. Those goddess also had older cults that predate their acceptance into the Olympian pantheon; the followers of those cults are druids or rangers.
The Tempest domain is especially appropriate for Zeus, since he monopolizes the lightning bolt as his weapon of choice. Poseidon could also be the god of maritime Tempest clerics.
Trickery domain is traditionally the province of Hermes, Aphrodite and Dionysus.
The War domain is appropriate both for Ares and Athena. Ares is inclined into the rage-based aspect of the warfare, while Athena is worried about tactics, logistic and weaponry.
The Death Domain is intended to be used only for NPC, but it could be used to represent Hades’ priests.
The Arcana Domain (SCAG) could be used to represent a Hecate priestess. This kind of cleric are in practice very rare; Hecate prefer to use sorcerers or sorceresses as her main followers
The Forge Domain(XGtE) is the main domain appropriate for Hephaestus’ priest.
The Grave Domain (XGtE) is similar to the Death domain. Hades is the main god of Death in greek mythology, but he has almost no priests or cult.
The Peace Domain(Tasha) can be used for more peaceful deities like Hestia or Asclepius.
The Twilight Domain don't seems to fit a specific mayor god, but it can be reflavored to cover the more ambiguous minor deities like Eos or Nemesis. Alternatively, Artemis has a strong lunar theme, and Apollo is the light god; they can be combined in a Artemis-Apollo priest.
Playtesting Archetypes
Both Athena and Hera has protective attributes; the Protection Domain could reflect their priests.
The Order Domain (UA) is appropriate for Athena, Zeus and Hera priests.