Here are three pokemon I've been testing out in this "new UU" tier:
Wynaut, Ursaring, Bibarel (obviously).
Wynaut has been quite awesome on my team. I've been using a rather weird EV spread, which lets me outspeed 0 Speed EV Spiritomb by 1 point, letting me shut off his CMs. Then, I used X-Act's defense EV applet to work the defense/hp EVs, because unlike Wobb, Wynaut actually does need HP EVs. I also use a Focus Sash to either Counter/Mirror Coat a strong hit, or so that I can Encore a Ghost move for Ursaring or Bibarel. I've been thinking about trying this strategy with a BD Linoone to complement it for a lategame sweep, but I haven't gotten around to it yet.
He's the thing that protects me from getting destroyed by Stall teams, because he can trap the pokemon, Encore what is most likely a support move, and then I can switch over to Bibarel and then pull off the Bread n' Butter Super Fang the switch-in combo. It took me a long time to get used to using Wynaut though, because unlike Wobb, he is very frail even with a lot of defensive EVs.
Wynaut doesn't seem nearly as dominating as Wobbuffet IMO. Unlike Wobb, he dies very quickly, and he can't come in several times either, so if his setup fails, he's most likely dead weight unless you carry a Wishpasser too. Also, there are quite a few things that carry U-Turn in UU right now, so Wynaut only really works against Walls or some setup sweepers (with very good prediction).
Ursaring has swept a few times for me. I use Facade/Close Combat/Crunch/Swords Dance w/Quick Feet and Toxic Orb. Facade is incredibly strong after a Swords Dance, even nearly 2HKOing Registeel after a Swords Dance with only max Attack and a Jolly nature. Close Combat murders any Normals/Steels/Rocks that try to wall Facade. Crunch takes care of Ghosts that wall Facade. Ursaring unfortunately does have problems with Spiritomb...
The biggest problem with this Ursaring is that he is absolutely screwed by anything that has Sub since Poison damage increases quickly. Also, he dies extremely quickly during his sweep, even without the help of the opponent. However, he is a good glass cannon sweeper. Remember though, Ursaring CAN be built to be very bulky, just that this particular one isn't.
Bibarel is my personal favourite, and he's always worked well for me in OU, so I thought, why not give him a shot in his home tier? I use my favourite set, which is Tauntarel (see the analysis for details). If there's something to get rid of annoying Toxic Spikes, this thing can work wonders. The basic strategy is to Taunt walls, cut them down with Super Fang, screw attackers with Swagger, stop support moves with more Taunting, etc.
It's interesting how many things it actually counters though. If you need a 100% counter for several Belly Drummers, Unaware ignores their Belly Drum, rendering foes like BellyZard useless. Problems with Cosmic Power Clefable? Bibarel doesn't mind, because Unaware ignores the Defensive boosts, and even then it doesn't matter because Super Fang would take off half current health anyway. He can stop most stat uppers and save the team from a sweep very easily. However, he does have trouble with stuff like Raikou for obvious reasons. Choice sweepers will also give him a problem too, though they will still risk 50% of their health coming off, or being Swaggered. Yawn is another good status in place of Swagger, since it can really stop sweeps by putting the opponent to sleep. However, Swagger is better considering how it functions with Unaware, and Yawn doesn't work after Sleep Clause as well.
Attempting to make a catchall counter for Chansey, Spiritomb and (especially) Registeel I tried a gimmicky combo of max Speed Tickle/Encore Wynaut and CB Trapinch.
Tauntarel can take these three just fine by himself for reasons mentioned above. :]
It may not seem like it can be Spiritomb, but unless Spiritomb has absolute max special attack and HP Fighting, it's going to be very difficult for Spiritomb to win. Bibarel can shut off Sleep Talk versions with Taunt, Swagger the hell out of the other ones, and is immune to one of the STAB moves, while not being affected by CM/NP boosts.