Cracks can develop between the pool deck and coping for a number of reasons, from shifting soil to failed expansion joints. Whatever the reason, allowing the crack to remain can cause further damage as the cracks expand. Because of this, make filling the cracks a high priority and do it as soon as possible. Epoxy grout is a quick set material that you can use to fill those cracks immediately. Made of epoxy and sand, it hardens firmly but still moves along with the stone of your deck, avoiding further cracking. In addition, it'll set quickly enough to allow you to use the pool in days rather than weeks after a cement based grout application.
Put on a pair of safety goggles, a face mask and work gloves before beginning the repair work to prevent injury from flying chips or to avoid inhaling concrete particles.
Modify the cracks to give the patch a structure that's more likely to hold it in place. Even out the width of the crack throughout its length, using a hammer and chisel. Create a uniform crack width of about 1/8 inch. Alter the slope of the crack using the hammer and chisel so that the crack flares slightly as it gains in depth. Having the bottom of the crack slightly wider than the top shapes the patch into a wedge. This wedge shape makes it more difficult for the patch to slip from the crack once it hardens.
Clean out the altered cracks with a nylon brush and remove the debris with a vacuum.
Mix a batch of epoxy grout using the mixing ratio provided by the grout manufacturer. Mix the two-part epoxy in a medium sized bucket until there are no longer any streaks through the mix, which indicates the presence of separate parts remaining. Use an electric drill with a paddle bit attached to aid in mixing. Add the sand to the epoxy to complete the grout, mixing in the material until you have a grout the consistency of peanut butter.
Fill the cracks with the epoxy grout, pressing the grout firmly into the cracks with a putty knife until it slightly overflows the top of the crack. Finish the patched surface using a trowel to level and smooth the patch out, blending it in with the pool deck. Allow the patch to cure completely for the curing time recommend by the grout manufacturer.