The best way I can see of doing this very briefly is thus:
- The Peloponnesians opt not to help the Athenian fleet, and as a result, Themistocles recieves Xerxes' ambassadors. Athens retains her democracy in exchange for the status of a Persian allied state, not formally under the control of the Satrap Mardonius.
- Aided by the Athenians, the huge Persian army invades the Peloponesos. Sparta attempts to resist, but this is stymied by a huge revolt by the Helots, and the Peloponnesian League soon collapses. Sparta herself is not occupied, but is stripped of her territory and helots, becoming part of the Satrapy of Greece.
- Various Greek revolts fail to flare up into life. Athens enjoys a long age of glory under Achaemenid protection, and democratic ideals spread throughout the world of the Persian occupied Aegean- with full respect for the Great King, of course.
- Over the course of the fifth century, the Persians subdue much of Thrace up to the Danube, and settle it with loyalist Greek colonists. Attempts to expand to the West, however, end in failure. The tyrannical and oligarchic states proudly proclaim themselves to be "free Greeks". True, they do not bow at the knee to an oriental despot- but then again, their peoples cannot control their own internal affairs as in democratic Persian Greece.
- By 350BC, despite occasional civil wars, the Achaemenid Empire is holding up well, without any serious rivals anywhere. Carthage and the Free Greeks are too divided, Macedon is part of the Empire, and various Egyptian revolts have been effectively stymied by the introduction of local democracy in the region. By 300BC, the entire Persian Empire is operating on a semi-democratic basis, at least at a local level.
Not your usual "Persia conquers Greece" scenario, but one that I think is a little more interesting than the usual stereotypical stuff.