You need tight control and mastery of how the CCs work. You need to determine which is easier for you, piloting the healer and letting the program drive the DPS out in front or conversely controlling the damage dealer and towing the healer behind you. Depending on your choice of classes one will be better than the other given the cool-downs you can use, interrupts available, etc.
Unfortunately, even if you get to the point where you can instinctively control your toon and psychically predict the botting toons actions, Arena is all about mobility, position and the denial of both. No CC can accommodate this. If you become comfortable with one of the two setups above you will do OK versus beginners but will get steamrolled by any team with just a modicum of experience. Your gear won't matter.
You might have better success with 3v3 than 2v2. This way at least two human brains are making decisions while the bot catches up with instant decisions the slow human brains may still be contemplating--and it also looks a lot less suspicious. Big Blizzard is watching and any kind of software assisted play in Arena is about the riskiest thing you can do with HB...
Hope this helps. If you really want to do this I suggest picking the CCs first and then rolling the classes they support instead of trying to find a "good" CC for any particular comp you happen to be in love with at the moment... Think paladin, shaman, druid... best of luck