The coach's award is an award given to the player who demonstrates the most leadership, sportsmanship, team spirit, and skill throughout the season. This person is chosen by the coach.
It would depend on whether it was used in the singular or plural. If it was an award for a single coach, it would be coach's but if it referred to an award earned jointly by two or more coaches, it...
It depends, actually, if it's: Coach's meeting - one coach's meeting Coaches' meeting - many coaches' meeting Coaches meeting - just a meeting of coaches.