What it does
Coba Berry only covers Flying: an opponent lands a super-effective Flying move on the holder, it gets halved, and the berry is eaten.
Flying punishes Grass, Fighting, and Bug. Those groups are full of common attackers and control mons — Grasses set up, Fighters get in your face, Bugs break — and they all fear a Flying hit. Brave Bird, Air Slash, or spread Hurricane on a 4×-weak Bug or Grass usually just KOs. Coba halves it, turning "blown away" into "still standing" so you can move that turn.
Flying has some nasty fast attackers in Champions (Talonflame's priority Brave Bird, assorted Flying STAB) built to remove Grasses and Fighters. Coba is for exactly those bad matchups.
Same split from Focus Sash as always: Sash needs full HP and dies to chip and spread; Coba works from any HP but only covers Flying. If you know a Flying move is coming, Coba is the steadier pick.
Who runs it
The carriers are Grasses, Fighters, and Bugs for whom Flying is lethal.
Gallade (7%), Fighting/Psychic, takes Flying as a major weakness — it wants to get in and click Sacred Sword, and its biggest fear is getting cleaned by a Flying move first. Coba lets it eat one and swing.
On the Grass side, Tsareena (1%), Venusaur (3%), Whimsicott (4%), and Sinistcha (3%) are all Flying-weak and take it to buy a turn for setup or control.
Bugs need it most: Ariados (5%), Bug/Poison, and Araquanid (1%), Bug/Water, both take Flying as a weakness and hurt from a hit to the face. Conkeldurr (2%), Fighting, is a slow strength core that needs Coba to eat a Flying hit and live long enough to Drain Punch back to health.
How to use it
The rule: hold it for that one Flying move.
With your berry-holding Grass or Fighter out and a Flying attacker across from you lining up Brave Bird, Air Slash, or spread Hurricane, eat the halved Flying, stay up, keep the turn.
Watch Hurricane in doubles: it hits both opponents, so if both your mons are Flying-weak and standing together, Coba only saves the holder. Don't stack two Flying weaknesses on the same side when building.
Against a Talonflame with priority Brave Bird, Coba is especially good — priority means you can't dodge it, you just eat it, and the halving usually leaves you alive to swing back.
Brave Bird also recoils the attacker, so after you tank the halved hit, that mon is chipped too and your swing back lands the kill more easily.
Tips & strategy
The best use is on an in-your-face Fighter like Gallade. It only deals damage up close, and opponents know Flying picks it off first — Coba drags that from "guaranteed KO" to "survives," and a living Gallade swings back with Sacred Sword or sets up Bulk Up.
Don't give it to anything Flying doesn't hit super-effectively. Coba only halves when Flying is super-effective; neutral or resisted, it does almost nothing.
Run the number first. A 4×-weak Bug at half is roughly 2×-weak, which is often just enough to live — but if the Flying attacker overkills hard (a boosted Hurricane, say), the halving won't save you. Then pivot out early instead of banking on the berry.