OK I gave this a lot of thought (more than I needed initially) and I've decided that I'll support only the following four types: Dragon, Ghost, Rock and Dark. The first three give CAP 11 perfect neutral coverage in OU with two STABs, while Dark means Heracross walls CAP 11's STABs, but that can be covered by a Flying move I guess. I think that perfect coverage is important because if we let CAP 11 get walled by something (say, Tentacruel), we risk creating a rival partnership that beats the partnership that we're trying to make. Remember, we're trying to make Togekiss's Perfect Mate, not Rotom-A's Perfect Mate or something like that. Since many of Togekiss's biggest foes are very popular, this WILL happen. So good luck convincing me to back a different type, lol.
Remember that there are ways to combat Electric and Ice moves other than the secondary type. The stat spread, especially Speed, can help against these; if CAP 11 outspeeds Zapdos, for example, it will need to take only one Thunderbolt. There are also the abilities Thick Fat and Volt Absorb (even Motor Drive if we think that it's necessary). There's also priority.
I'm kind of leaning towards Dragon because the Electric resistance will ease the pressure on future discussions to check Jolteon. However, I do understand the concerns over it possibly being overpowered. We have made a Dragon CAP before, though. We'll see what happens.
(EDIT: After hearing a lot of good arguments against Dragon, including but not limited to the recent ones from reachzero, Rock has become the frontrunner in my eyes. It would be nice to have more freedom against Dragonite, and with the sizable offenses CAP 11 will need against Zapdos, Dragon probably would be overpowered. The sandstorm boost helped to put Rock over Ghost. Now, remember that Togekiss can't control whether or not Sandstorm is up. This means that if CAP 11 benefits from Sandstorm, that can only be a good thing.)
I envision the following happening:
Togekiss switches in. The opponent switches in a counter to wall Togekiss, forcing it out. In comes CAP 11. CAP 11 has perfect-coverage STABs, so it can compel the Togekiss counter to stay in to minimize the damage done, or protect the counter to let CAP 11 wreck for a while. After that, Togekiss cleans up.
Now, of course I'm not saying that these two Pokémon should sweep the entire metagame. Every Pokémon gets worn down if it has to face more than one opponent. That's for the other four Pokémon to address.