There are quite a lot of viable types to use in this situation. I'll just give my two cents on those that have been mentioned to a great extent in this thread already:
Electric: This is an okay choice. I think the "only Ground weakness" argument is kind of over-exaggerated, to be honest. Sure, a big part of core duos is switching in on immunities and resistances. However, the neutrality of Electric types, in general, actually cause a disadvantage to Togekiss. Those who attack an Electric type usually finds (with the exception of Magnezone) that any attack will come its way and hit hard, Super Effective or not. Now, Togekiss is immune to Ground and Ghost, and resists Grass and Bug. That's not really awesome, to be honest, and an Electric CAP11 can only force the Ground immunity for Togekiss. Tyranitar can easily Stone Edge or Crunch CAP11 and hit Togekiss for big damage. Also keep in mind that Electric attacks provide little insurance against Togekiss' counters (Electric is used for bulky Waters and Gyarados mostly, which Togekiss has little trouble with except Gyarados). Resisting Electric itself is okay, but unlike my stance for CAP10, I don't like Electric's neutrality here. What will Electric bring to the table that will help Togekiss? Is it really only Ground attacks and an Electric resist?
Steel: Eh...no. Steel provides no offensive support whatsoever STAB-wise obviously, so I'll leave that out of the equation. Defensively, Steels are weak to Fighting, Ground, and Fire. It resists Bug, Ghost, Dark, Psychic, Grass, Normal, Dragon, and Rock. Out of those resistances, Bug, Ghost, and Grass are also resisted by Togekiss, so they are meaningless. Of those resistances, Normal, Dark, Psychic, and Dragon hit neutrally on Togekiss, which makes them moderately important. Rock *EDIT* and Ice are the only Super Effective moves where a Steel can enter from Togekiss "safely", as in without significant bulk. Meanwhile, like Electric, Ground is the only move where Togekiss can enter safely. Fire and Fighting still hit hard. I'm not seeing a whole lot of synergy here, and don't forget Steel's offensive unimportance. Throwing resistances on a Pokemon does not constitute "synergy".
Psychic: I'm not too sold on how useful a Ghost weakness is for Togekiss' success, especially since (to my knowlege) only two Pokemon in the OU metagame really use Ghost moves and usually carry a move that hits Togekiss super effectively. Bug moves are also mostly physical (at least the most threatening ones are), and taking 33% from U-Turn plus a SR weakness doesn't seem to convince me that it's safe to switch Togekiss into something like Scizor, who greatly troubles Psychic types. Meanwhile, resisting Fighting is nice, but with weaknesses to Electric, Ice, and Rock, I feel there are more pressing needs for Togekiss to find in a partner. Resisting a neutrality is not an importance. I want to like this, but I'm not feeling it.
Poision: Not feeling it. It's like Electric, but doesn't resist Electric. Heck, even Toxic Spikes aren't an issue for Togekiss. There are no benefits here, other than the "benefit" of bringing in Ground attacks. Once again, resisting a neutrality is far from important.
Rock: I think Rock is a decent choice. Rock is weak to Water, Grass, Fighting, Ground, and Steel. Rock resists Normal, Flying, Poison, and Fighting. What I like most about Rock is the "small things" about it: the Sandstorm 1.5x SpD boost and immunity to passive damage, for instance, can take advantage of opposing TTar and Stall quite well, while giving it some natural SpD bulk so that when BST conversations start, we can focus on other non-natural factors. STAB Rock attack is nice offensively, and hits counters to Togekiss hard like Zapdos and such. Togekiss easily switches into Grass and Ground, and doesn't mind Specially-based Water attacks. The drawbacks are the Steel weakness, which makes Scizor a main target, and the Fighting weakness, which while neutral to Togekiss, doesn't help. However, Scizor troubles aren't only solved by typing, however. Individual Pokemon concerns are valid, but aren't mandatory for typing discussion. I would support Rock.
Dark: Much like Steel, a Fighting weakness and neutrality/lack of opportunities to switch makes me say no to this. I don't see much positives.
Fighting: I think this is an okay choice, much like Electric. Resisting Rock is good, and having a powerful offensive STAB for counters is nice. However, neutrality once again kills it, and really, Togekiss can't switch in on anything that's aimed at Fighting types, and trying to predict will be impossible because of neutrality. I'm not seeing much synergy and positiveness here, although there are some useful aspects.
Ground: I also think Ground is a decent choice. Ground is weak to Water, Grass, and Ice. It resists Rock and Poison, and is immune to Electric. I find it extremely interesting that Ground's short list of resistances and weaknesses actually cater to Togekiss quite nicely. Ground resists Rock and is immune to Electric, which covers almost all of Togekiss' initial weaknesses. Meanwhile, Togekiss resists Grass and doesn't mind specially-based Water attacks. Ground is a nice offensive STAB, obviously. I find Rock a little bit more useful in terms of Togekiss' counters, but Ground does well against grounded Steels, which is awesome. What prevents this from being the obvious choice is the shared Ice weakness, which in a metagame that centralizes on Dragons and Ice-weaks and countering them, is very detrimental. An Ice weakness going to be a problem no matter what, so it's hard to simply just excuse it. Aside from this, it's a good choice.
Fire: Not seeing the usefulness defensively here. Dual SR weakness is obvious, and even with "we can just secondary type it", it's too centralizing, and we're reduced to having a maximum of a neutrality. I don't like starting off on that foot. Offensively, it's a decent choice however, hitting Steels bar Heatran hard. I actually think this has some promise offensively, but will give us trouble defensively no matter what the secondary typing is. I'd say it's okay, but not good.
In conclusion, I would support Ground and Rock first and foremost, and give weak support to Electric, Fighting, and Fire.