To find the rate of change in the diver's depth, we divide the change in depth by the time it took to make that change. The change in depth is 10 meters (because the diver saw something interesting 10 meters lower) and the time it took is 10.1 seconds.
Therefore, the rate of change in the diver's depth is $10/10.1 \approx \boxed{0.99}$ meters per second.