Kirby doesn't belong at the bottom by any stretch of the imagination. SH forward+b is a terrible idea in singles, but in doubles? Forces both opponents into their shields leaving one open for a grab by the other player. Suicides make a world of difference and they're easier to land because it's more chaotic. As Samochan said, his ability to keep opponents off the stage is magnified because he has another teammate capable of getting them there. He has 3 options for additional powers. With Falco's lasers, he can consistently save a teammate. Using the first part of his f-air will barely nudge somebody, giving them more recovery room. His roll is fast and covers a lot of ground, so he can traverse the stage relatively safe. He makes a spectacular teammate played properly.
IC's at bottom? Two words, CHU DAT. Or, if you want more in depth reasons... their smashes are potent KO'ers and their wavedash gives them the opportunity to glide around the level, punishing mistakes. They can make their movements hard to read, so you can keep the opponent guessing when you suddenly dart back to help your teammate. They work particularly well with a teammate who focuses mostly on an air game, because they can cover the ground with strong, relatively safe attacks. They're also reasonably heavy, which makes them good for holding stock. Furthermore, their recovery is hindered by edgeguarding less because with a teammate to distract the opponent, it becomes significantly harder to punish their forward+b.
Jigglypuff should definitely be high up in the teams list, just because she can attack without committment. This means that she can maneuver around the stage with disruptive hits while always being able to travel in another direction to help a teammate. Also, if a teammate lands a grab, just rest, then jab to wake her up. Free stock right there.
Peach is a nice teammate because she can float and use d-air to help a teammate's recovery. Her down-smash takes up a nice part of the stage, and in the chaos of 2v2 it's a lot harder for an opponent not to accidentally CC and take 30-60 damage. With decent DI, she lives quite a while, and she can make herself difficult to edgeguard while a teammate comes in to help. Her high priority attacks, when the opponent can't focus on spacing as much, will often cut through the action.
Fox; he has those important KO moves: shines, u-smash, and u-air. If an opponent is being difficult, shine them off the stage to help your teammate. If somebody's taking too long to kill, surprise up-smash. Up-throw up-air works on a large portion of the cast, and will also KO at reasonable percentages. Shines can turn the tide of a match with remarkable quickness. His general speed gives him the ability to cross the stage in an instant, often with one of his powerful KO moves, or with his speedy aerials. He definitely belongs way up there.
Those are the characters I know the most about, simply because I team with them, have seen them, or use them myself in teams.
As for the usefulness of this list: of course you're not going to get the full impact of a teammate's usefulness just from their position on the list. The singles tier list itself is hardly an indication of individual matchups, just a reflection of general tendencies and advantages. The 2v2 tier list, therefore, would be an indication of how well a character can work with others, and how their inherent abilities are magnified or diminished in a 2v2 setting. It's probably a useful thing to have around.