4 elements that a player needs in a coach
Knowledge of the game
I often consider good coaches as the ones that are tennis 'geeks'. These sort of coaches are ones that study the game, not just in their uptime, but also during their downtime. They are fans of the sport and they watch it vigorously. There is a difference between a passionate coach and a coach that's passionate about Tennis. Both elements are so important, but there are lots of coaches who are passionate about their job but may not be passionate about the game. Coaches who love the game, watch a lot of Tennis, they're constantly improving their own development and are always looking at things to improve on. This pays dividends for the development of the player.
Puts equal effort & time into every player
In most cases, good coaches are coaching numerous players, especially if they are in high demand. However, a commonality that often occurs is that coaches have their 'favorites', and this can affect the other players. Putting equal time and effort into each player is massively important. Just because one of the players is weaker, doesn't mean they can't succeed if given equal attention.
The coach values the 'team'
The average Tennis player has a team around them. They may be conscious of this team, or maybe not. I consider a team as the: Parents, siblings, main coach, Fitness coach, head coach, and possibly more if we go into detail such as nutritionists etc. Many coaches don't honor each relationship and can often devalue members of the team, which can substantially affect the performance of the player. Coaches should work in tandem with parents especially, as it's the parents that are going to be the driving force behind the tournament plan, number of lessons, transport, nutrition etc.
Goes the extra mile
Things that I consider as going the extra mile are making phone calls after every match if the coach isn't present, regular meetings to discuss goals and plans, coaching the 'lifestyle' of the player, chats with other coaches to discuss progress or problems, takes interest in issues outside of Tennis and trying to consistently take part in tournament visits.