Place a small chunk of limestone on a work surface. Take a hammer and gently pound pieces of the stone off, crushing it to a powder similar in size to granules of sugar. Make enough powder to form a filler for the crack.
Run a wet sponge over the cracked area of the limestone stair, moistening it and the area around it.
Place the limestone powder onto a tile or other clean work surface. Add wood adhesive, mixing it in with the powder using a putty knife. Add the adhesive until it forms a paste.
Fill the crack on the limestone stair by pushing the paste into it. Apply until it reaches the surface of the crack. Leave the paste to dry overnight. Sand away any excess until the stair riser and tread are smooth.