The black cat is purchasable at Eeylops Owl Emporium & Magical Menagerie. It is sold at 9 Galleons. When bought, it becomes your avatar.
Description[]
"Black cats make loyal, charming pets."
Pottermore PlayStation Home[]
On Pottermore PlayStation Home, the Black Cat is one of the five cats available for purchase at the Magical Menagerie. It must be purchased with real money and costs £2.39.
When purchased, it will walk alongside the player's avatar in the game.