Special coaches appear from time to time and are in town to teach young players different things. Depending on their purpose, coaches can train certain players. Those criteria are connected with player’s current role, special ability or similar. If a player is not compatible with the coach, he will appear as greyed out. However, even if you do not have an option to hire a specific special coach, you can always check out the available ones, or wait for some new coach to come.
Also, a rule not to forget is that each special coach can only be assigned to one player, so choose wisely!