Assuming this is due to his desire to get better and not your desire to see him get better.
I would suggest hill sprints and strength training, speed is correlated with strength.
All good strength programs work by doing the same exercises over and over and gradually increasing weight and repetitions while training to failure or near failure. Pick a program and stick to it for 3 months (which is more important than which program you pick). Do the workouts with him, it's good for both of you.
People all have their favorite strength routines. My workouts are currently focused on single leg lifts (in large part because I am rehabbing a knee injury) so single leg deadlifts, Bulgarian split squats, pistol squats, single leg toe raises, lunges.
I would stay away from barbells and use dumbbells or kettle bells. I would recommend general athleticism and strength rather than anything running specific.