You cannot get a trampoline in any Nintendogs game (Nintendogs, Nintendogs + Cats). The series focuses on realistic pet simulation: walking, training via voice commands, competing in disc competitions and obedience trials, grooming, and simple touch-based play (fetch, bubbles, tug-of-war).
While real dogs might enjoy a trampoline, the game's physics and scope don't include large outdoor equipment. The closest "bouncy" fun is the high-jump trick or the trampoline-like animation when a dog pounces on a toy.