First of all, I'd like to address a point here. Togekiss and CAP11 don't need to beat the whole opposing team by themselves! CeleTran can't do that. SkarmBliss can't do that. No two-Pokemon combination can do that. If it could, one or both would likely be Uber. It'd be perfectly okay if we need a third Pokemon to close a few holes. For instance, if CAP11 is weak to Water and Fighting, it's perfectly fine if the third member of our team is Celebi or Gyarados. What we do need CAP11 to do is to mitigate Togekiss' biggest problems.
Togekiss' biggest problems come in the form of Rotom-a, Zapdos, Jolteon, and as smallvizier astutely mentioned, Dragonite (which could be a much bigger factor than you think, pending Salamence's status). All of these except Dragonite share some common characteristics: they are neutral at worst to both Rock and Dark, they are Special attackers. Sadly, Dragonite is so different from the others that there is very little we can do without choosing Ice, which while mildly intriguing for the neutrality to Ice and effectiveness against Zapdos and Dragonite is really handicapped defensively compared to our other choices. Fortunately, Rock is a great choice for dealing with Togekiss' counters, again excepting Dragonite. Getting a SpD boost in Sandstorm makes a huge difference when it comes to taking one or two Specs Thunderbolts from Jolteon, which is a lot harder than you might think. With this is mind, Rock has my full support. Dark seems handy from an offensive standpoint, but it definitely does much less for CAP11 defensively than Rock does. Dragon is definitely tempting for the Electric resist, but consider this: it needs to be able to beat Zapdos. Suppose the Zapdos in question is SubRoost Zapdos. Zapdos is incredibly hard to kill if the other Pokemon is slower, and it runs 328 speed. Even so, Jolly Life Orb Salamence can't quite OHKO full health Zapdos with Life Orb, nor can (new) MixMence Draco Meteor. So if we're slower, good luck trying to KO Zapdos without offenses better than Salamence. So in other words, no Dragon/Fighting type strong enough to have a realistic chance of beating Zapdos is weak enough to be a really balanced Pokemon.
"But Rock can't beat bulky waters, and is weak to Fighting!"
Read my first paragraph again. I should also point out that Togekiss does just fine against most bulky waters, it's only really offensive Suicune that gives it any problems. Even with a neutral nature and no SpA EVs, +2 Air Slash does 43.8% - 51.8% to Vaporeon, which is plenty as far as I'm concerned, considering the 60% flinch rate.
tl;dr, Rock is the best choice for dealing with the Pokemon that give Togekiss problems.