Overhead exercise prescription, like any, begins with evaluation. Overhead pressing and weightlifting movements like the snatch and jerk are often prescribed with little hesitation. These movements require exceptional shoulder mechanics, and unfortunately, I believe, coaches already have a place for these movements in their programs before they ever see their athletes. Think about all of the variables that go into allowing the arm to elevate safely above shoulder height: lumbar and thoracic spine posture, scapular mobility/stability, and glenohumeral stability/mobility. Each of those variables has a number of contributing factors. If there is dysfunction at any segment, loaded overhead exercise will become unsafe. So what does this all mean..
The overhead squat test is a great movement screen. Normally it's done with a dowel or pvc, but I rather do it without a dowel and even with a very light dumbell in each hand. This allows for better evaluation between sides. If an athlete cannot overhead squat well without a pvc, barbell snatches and jerks are probably not a good place to start.
If your OH squat test reveals that an athlete cannot not maintain good arm position (arms move forward, humerus rotates medially), look at thoracic mobility, and functioning of the scapula and glenohumeral stabilizers, mainly the lower/middle traps, serratus and rotator cuff. Isolate those muscles first with exercises like supine Y's, prone Ts, wall slides (facing and facing away versions), and side-lying external rotation. Use 3-5 second iso holds and low reps to begin.
As you work on strengthening the smaller muscles in isolation, incorporate overhead iso-holds with light weight into multijoint exercises. 1-arm DB overhead squats, 2-arm DB OH squats, and DB OH lunge versions can all be used to begin to establish OH stability.
Periodically retest your athletes to see how they're improving. Again, if your athletes can't move properly without additional resistance, your forcing the issue by loading them too soon. There are safer alternatives to every exercise. The purpose of your program does not have to change, just 1 or 2 exercises, and that's a pretty fair trade.