Kiddy League Coach is the true antagonist of the Buffy episode "Nightmares", despite him not appearing until near the end of the episode. His actions however were directly responsible for the events of the episode: he is never named in the episode and is simply known as the Kiddy League Coach.
He is the second evil Coach in Buffy canon (with the other being the swim coach from "Go Fish").
The Kiddy League Coach beat a young boy under his care named Billy Palmer into a coma for losing a game. As a result, Billy became trapped in an astral nightmare, trying to confront his fears — which manifested as the "Ugly Man". Because of the Hellmouth's power, Billy's dreams began to manifest into the real world and many of Sunnydale's residents became ensnared in their own living nightmares.
After confronting her own nightmares, Buffy fought the "Ugly Man" and knocked him out. She then convinced Billy to face the monster. When Billy did so, his nightmare ended and he miracolously awoke from the coma; as he awoke, Sunnydale returned to relative normality (at least for Sunnydale, anyway).
However, as Billy awoke, the Kiddy League Coach entered his room, not suspecting Billy to be recovered and likely trying to either finish Billy off to cover his track or otherwise ensure Billy didn't wake up (or at minimum remember the attack).
Buffy confronts him and reveals that she knew he had beaten Billy after the game, at first he tried to deny it only for Billy to finally confront him personally - the boy confirming the crime, prompting the Coach to try and flee the scene but is stopped by Giles and Xander. Later, he is revealed to have been taken away by authorities after Billy informed them of what had happened to him.