If you can't reglue a split baluster, carefully saw through it and remove both parts by "working" them out of their sockets.

Buy or make a replacement baluster and cut it so that it is 1/4 to 3/8 inch longer than the original.

Bore the existing top hole in the handrail 1/2 inch deeper, but take care not to bore through the top of the rail.

You should be able to insert the baluster into the top hole far enough to allow the bottom end to drop into its socket. Glue and nail the replacement into the sockets.