Cover your eyes with protective gear, such as goggles, to prevent injury from flying debris.
Break the grout between the damaged coping with a chisel and hammer. Chisel around the coping to pry it loose from the mortar bed, and use a reciprocating saw if grout is not coming off easily. As you remove the coping, take care not to drop chunks of stone or mortar into the pool.
Remove the coping from the trim once it is loosened. Brush away any remaining debris from the bed with a stiff bristled brush, and chip away any jagged edges with a chisel.
Mix thinset in a mixing tub according to manufacturer's instructions. With a brick trowel, add a 1/2-inch layer of thinset to the surface of the bed. Set the coping stone into the thinset and press down to remove any air bubbles from underneath the stone.
Fill between the stones with thinset, and take care not to get any on the surface of the stone. Wipe the stones with a damp rag if some thinset gets on the surface. Allow the thinset to fully harden before you step or pull on the coping while swimming.