I'm going Mythbusters on this one, please read this!
Togekiss loses to it's weaknesses; Rock, Electric and Ice kill it:
False to an extent. There's one Rock type in OU to care about, Tyranitar and he dies to Aura Sphere no problem; plus Cap11 is a Fighting type at least, no worries here. All other Rock attacks will be coming from non-STAB sources and it they aren't Ground types, they can be paralyzed and taken care of. Togekiss can take unSTAB Stone Edge too and Roost it off (also moves the weakness) to boot; this holds true for the Stealth Rock weakness too. Common Ice and Electric users suffer the same fate baring Jolteon and Electivire and Mamoswine. But if you opt for Aura Sphere over Thunder Wave, all of a sudden Rotom-A and Zapdos are the main threats. Paralysis support helps all of these. To prove my point, let's use Starmie, a Pokemon mentioned as "killing those combos". Starmie comes in, you paralyze it and it can't do a damn thing thanks to Roost.
Togekiss loses to things that resist Air Slash:
Togekiss is special in that it can beat ANYTHING that can be paralyzed (preferably by Thunder Wave) and/or Flinched. Blissey can be set up on without a problem. Even Rotom can have trouble if you get it slowed down (Rest-Talkers can be problematic). Togekiss abuses Serene Grace and can win battles she has no business winning, this happens a lot more than you think. While Togekiss dislikes Flying/Fighting Resistors, she can over come all of them with the right set. Don't under estimate a STAB move coming of a base 125 SpAtk with NP.
The two points are to not worry about covering Togekiss' weaknesses perfectly and to assume she needs massive help offensively. Really, many types will work here; which brings me to my final point.
Be careful of making a better partner for Zapdos, Skarmory, Gliscor, or Gyarados than Togekiss. We have Rock resists which all of them appreciate to a degree. We must be careful not to make any of them too good defensively with out second type, particularly Gyarados. Electric is not a good move in this regard as that helps all of them except Gliscor.
This is why I like Fire. It removes the Rock resist for all the Flying types to enjoy (Togekiss really doesn't need that compliment). It adds an Ice resist but also Water so Gliscor can't pair up easily. It doesn't stop Electric (which Togekiss cares about but not as much as you'd think) so Gyarados can't take advantage, plus it doesn't help CAP11 take on bulky Waters. Fire also helps take care of every single remaining counter to Togekiss. Steel types, Ghost-types, Zapdos. Yes, it leaves holes but it's a very well rounded option, particularly offensively which is a direction I feel we are going to explore.