Sigh. Apparently, posting articles written by respected strength training coaches is taboo around here. I guess we should all listen to the geniuses on this forum instead of, you know, experts. But, in the slim chance that you can take the time to read and - gasp - even learn something today, here is some more food for thought about "core stability" training:
The Myth of Core Stability: a long, well referenced paper that talks about the total lack of scientific evidence regarding "core" training. Primarily focuses on the fact that training the abdominals has no effect on back pain, which is why my first set of questions to the OP was WHY he wanted to train his core.
Fitness Myth Busted: Core Stability and the Bosu: references a study that shows that with equal loads, there is no significant difference in core muscle activation between the BOSU and a solid platform for a number of exercises. And since people typically use VERY light loads on the BOSU, there will be very little activation of the trunk muscles. The BOSU might improve your balance - which is not without merit - but it is NOT an effective tool for core stability or strength.
Core Stability or Pure Stupidity?: references statements from numerous papers that talk about very flawed basis of "core" training: that real world actions don't isolate particular muscle groups, that abdominal activity does not play a strong role in spinal stability and that "the world of core stabilisation currently remains far too heavily based in marketing and belief than in valid science."
The point of the Rippetoe article I linked originally was not that squats/deadlifts/etc are the only way to train the core, but rather that most of the other "core exercises" people are doing these days are definitely NOT the way to train the core. Working on a BOSU or stability ball just don't allow for the kind of progressive loading that is necessary to produce strength gains. Barbell training is one medium that does allow this, but not the only one. For example, gymnastics is another great way to strengthen the core because you can progressively increase the difficulty. Finally, as explained in all the articles above, training the core in isolation makes no sense. It isn't effective, it doesn't help with injury prevention and it won't help athletic performance. All of those goals can only be effectively achieved with a routine that trains the entire body.