I keep odd pieces of walnut around just for this kind of stuff. Cut off butts from recoil pad installation work great.
Splinter off a few pieces and tap them tightly into the hole with some waterproof glue or epoxy. After the repair is cured, cut the splinters off even with the stock drill a pilot hole for the screw and install.
I have done it all at once a few times, as well, putting just enough splinters in the hole to make a good tight fit for the screw. Cut them a bit shorter than the hole, add the glue and install the screw.
Saves drilling a pilot hole after curing, but be sure to put some paste wax on the screw as Mauser98 has posted, or the screw will be in there permanently.
Ted