In order to answer this question we must first understand the function of the core during movement. For our purposes consider the core as the muscles, superficial and deep, in the abdomen, back, glutes and hips. During a movement the core is used as a link that transfers forces throughout the body. The more efficient the transfer of force is, the better the athlete can perform. Now, let’s discuss the best way to train this transfer of force for sport specific movements and lifting movements performed in the weight room.
Unfortunately there is not a concrete answer. However, completing the sport specific movements required by an athlete’s sport may be enough to ensure an efficient transfer of force and increase core strength. For example, increased core strength has been shown to help decrease the amount of time it takes an athlete to sprint 40 yards and completing 40 yard sprints helps increase core strength. As for increasing an athlete’s ability to perform Olympic and high intensity (via increased weight) lifting movements, extra core strengthening exercises as well as completing the lifts themselves would be beneficial. The core can be trained to increase strength like all other muscles groups; with a higher intensity or resistance and at least 48 hours of rest to repair micro tears before training again.
Would extra stability exercises such as using unstable surfaces help? Yes, they would, but time might be better spent doing lifts on a stable surface. Although you may not be activating as much of your core on a stable surface as you would on an unstable surface, you are producing much more force and lifting much heavier weights. Developing strength and power is crucial for sports performance and they can be best developed on a stable surface. Compound or Olympic lifts that activate your core and have a greater transfer of force throughout the body (Deadlifts, Squats) work great to help strengthen your core and would work well in conjunction with sport specific tasks.