Besides the monk's class feature “Stunning Strike”, how can a player character cause the stunned condition? I am looking for a solution other than very rare or legendary magic items or any Unearthed Arcana. Spells or other class features are ideal.
5 spells, the Monk's Stunning Strike, and a few items.
The only ways, disregarding items, to stun a creature are the Monk's Stunning Strike (PHB):
The target must succeed on a Constitution saving throw or be stunned until the end of your next turn
The Contagion (PHB) spell:
In addition, whenever the creature takes damage, it is stunned until the end of its next turn.
The Divine Word (PHB) spell:
30 hit points or fewer: blinded, deafened, and stunned for 1 hour
The Psychic Scream (XGtE, 163) spell:
On a failed save, a target takes 14d6 psychic damage and is stunned.
The PW: Stun (PHB) spell:
If the target has 150 hit points or fewer, it is stunned.
The Symbol (PHB) spell:
Each target must make a Wisdom saving throw and becomes stunned for 1 minute on a failed save.
Including items, the DMG lists the Legendary Hammer of Thunderbolts, the very rare Robe of Scintillating Colors, the very rare Staff of Thunder and Lightning, the rare Wand of Wonder (only stuns you, though), and the legendary Whelm.
The Princes of the Apocalypse book also has an uncommon Storm Boomerang that stuns (credit to NautArch for finding this):
On a hit, the boomerang deals 1d4 bludgeoning Dmg and 3d4 thunder Dmg, and the target must succeed on a DC 10 CON saving throw or be stunned until the end of its next turn.
There are plenty of (high-level) spells that cause this condition
Many stun abilities come from spells (ranging from 5th to 9th), including:
A list of all spells that inflict the stunned condition, and one that removes it, can be found here.