Found one! https://bulbapedia.bulbagarden.net/wiki/EP092
Passive is an interesting word. The games aren't really that suggestive of a Pokémon's demeanour, since anything obeys without question, mostly. The Bulbapedia entry states that the Pokémon is known for its vicious temperament and is often prone to violence, which is often the case in the anime. However, passive would imply more than just obedience, it would imply the Pokémon is friendly to its trainer and not prone to confrontation. There are Gyarados under ownership of many trainers, including Lance, Clair, and Wake, but given they are trained for combat, they are more assertive in their behaviour despite being tame.
This one, that evolved from an abnormally large Magikarp, looks like a good candidate, about as much affection as you could possibly see from the "atrocious Pokémon".