You gotta go all in on keeping the opponent from launching their spells. Cockatrice is a one-troop wrecking crew on Yellow days: Drain mana, Entangle, and usually refill himself if you drain 10+? Oh, and do double damage to entangled enemies. He's enough to shut down nearly all the spell casting all by himself.
Plus you've got a few options: The Devoted is good to keep your front-line Cockatrice alive and charged up, while cleansing everyone. Herdmaster, Great Maw, Garuda, all excellent.
I usually use Elspeth and my Deathknight hero... first turn, blow up the hero, charge up Cockatrice (and probably the second troop) instantly, and Death Mark the entire enemy team. Plus I've got another troop slot to mix and match depending on the opponent.
Yeah enemy Deathknight is irritating, but if you're locking down the whole enemy team (constant mana drains + Entangle), you can put in a direct damage troop (this week Paladin is my weapon of choice) to execute all the non-Hero enemy troops first.
You don't even need to worry about Impervious troops or summoners because the opponent never gets far enough for it to matter.
Yellow day is one of my favorites. You don't even need Famine or Stonehammer to dominate with a little strategic planning.