In-depth descriptions of each concept are here.
Concept: Stall-breaker
Analysis: Since the ban of Salamence, stall has become very popular in the metagame. There are good mixed attackers like Infernape who do a good job of stopping stall, but I don't think there is a pokémon who does the job perfectly. I'll admit that I don't know everything about stalling, but I think a fast poison type with perish song/taunt would be cool to use to combat the stall. I know you don't like ability talk at this point, but Cloud Nine would be a good ability for it.
Concept: Anti-Hax
Analysis: Hax is something that everyone and their mother complains about. It ruins what could be good games, a freeze comes in, Jirachi flinches through three of your Pokemon, a miss decides the game or a crit turns the entire tide of a match-up, or possibly TWave decides that you really need to stay para'd while your opponent gets a +6/+6 DDMence. Why not have a Pokemon that you could switch into all this oncoming hax and prevent it from ever happening? Something that could absorb that TWave, and stop flinch fests, or prevent moves from missing? This would take an extremely complicated combination of moves, stats, and abilities, but if done right this could be exactly what the metagame is looking for.
Name: Reliable Status Inficter
Analysis: The Pokemon games possess many different status inflicting moves, from Thunder Wave to Toxic, Hypnosis to Will-O-Wisp. There are very few Pokemon which have access to a wide variety of status inflincting moves, and even fewer who can pull it off successfully. Most status moves suffer from a lack of reliability: 75 is a normal stat for a status inflicting move not named Thunder Wave or Confuse Ray.
However, there are several abilities which help boost accuracy or increase the chance of a move's secondary effect activating. For example: Compoundeyes. This ability raises all of the Pokemon's attack accuracy by 30%, which eliminates the unreliable accuracy troubles of moves like Sleep Powder and Will-O-Wisp. No Guard also stands out, raising the accuracy of all moves to 100%. Serene grace would be an interesting addition if we wanted this CAP to go a more offensive route.
With a good speed stat and a reasonable amount of defense, the Reliable Status Inflicter would have no problem outrunning and crippling a Physical sweeper with a burn, or prevent a wall from setting up. In theory, a reliable status inflicter could plug your team's weak spots.
Extra: I'm pretty sure there's no other Pokemon which fills this role successfully. I've seen dual status sets on plenty of UU and NU sets, but I'm not sure how well they work, if it all. It's a cool idea, I think, and has interesting potential in the competitive scene.
Balancing it could be tricky. Would super-fast status moves be broken?
Would increased accuracy on a Pokemon with strong offensive stats be too good?
Would a Pokemon like this even be useful, or just an interesting novelty?
Name: Psych Up Abuser
Analysis: The ability to raise stats in the metagame is always something you strive for, weather it be Agility to out speed and sweep, DD for GDos or TTar or Curse for any slow but bulky physical attacker. But what if you could use their gain to your advantage? Come in and steal their boosts and retaliate with your own attack to scare them away. Let them do the work for you.
Name: Anti-Trap
Analysis: Pursuit sucks, Wynaut sucks, getting your scizor killed by magnezone sucks, etc. Essentially this pokemon would make trappers much less viable. One possbile option would be to use trace to trap Magnezone and dugtrio and then turn them into set-up bait. Another option is to counter trappers and pursuiters so that if they did trap and kill one of your pokemon then they'd be put at a sizable disadvantage.
I imagine this pokemon would be only mediocre without the prescence of an enemy trapper.
Name: Flying Immune SR
Analysis: Most flying types are hurt pretty bad by the prelevance of SR. Their use is no where close to as good if SR is in play (prime example, Staraptor). Making a Flying type poke immune to SR could seriously shake things up as it now has no fear of switching in because of SR, let alone having a secondary Flying type is not a bad defensive typing.
Concept: Sunnyside Up
Analysis: Face it. Sunny Day sucks in the OU metagame. Sandstorm has Tyranitar, and benefits a bunch of appropriate Pokemon. Hail has Abomasnow and to a lesser extent Walrein, Froslass, and Mamoswine. Rain became a dominant force by Kingdra itself, and not only that but there are more viable sweepers under the Rain such as Kabutops and Ludicolo, etc. The problem with Sunny Day is that the benefits are just too wrongly distributed. Grass-types who through Cholorphyll benefit the most from Sunny Day and Solarbeam are absolutely murdered by the 50% boost in Fire-type attacks. The Fire-type Pokemon who enjoy the said boost will also gain a 50% resistance to Water-type attacks, but lack the Speed increase. How could we craft such a Pokemon so that it gains the benefits of Sunny Day, while keeping it viable in the metagame?
Extra: Taking note, this is basically a "Kingdra in the Sun" concept. A Pokemon who through typing, ability, and stats would be able to fully abuse the weather and benefits of Sunny Day.