I ship Butters with Kenny because they're both good boys and they deserve each other. As for interactions, they're rare but that just makes them more special. Since people keep asking, I'm just going to make a list.
Kenny Dies: Butters draws a cute picture of himself and Kenny in an airplane.
Jared Has Aides: Butters feels insecure when the boys compare him to Kenny.
Freak Strike: Butters wears Kenny's parka.
Lil Crime Stoppers: Kenny plays good cop and comforts Butters during his interrogation, making him smile.
Good Times With Weapons: Kenny accidentally gets a ninja star stuck in Butters eye.
Guitar Queer-O: Kenny and Butters hug when Stan and Kyle beat the game.
Major Boobage: Butters takes care of Kenny and comforts him while he's sick from cheesing.
Eek, a Penis!: They play in the sandbox together, Butters smiles at Kenny but looks down with a scared expression when Kenny looks at him.
The Ring: Butters gets upset when he finds out Kenny has a girlfriend and tells the boys she gives BJs, but then it turns out he doesn't even know what BJs are.
The Coon: Chaos and Mysterion fight, Butters is a wimp anyway but Kenny is clearly holding back.