Kiddy League Coach is the main antagonist of the Buffy the Vampire Slayer 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 after his team lost a baseball 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 miraculously awoke from the coma; as he awoke, Sunnydale returned to relative normality (at least for Sunnydale, anyway).
However, as Billy did so, the Kiddy League Coach entered his room, not suspecting Billy to be recovered, and likely trying to either finish Billy off in order to cover up his tracks, or otherwise ensure Billy didn't wake up (or at minimum remember the attack).
Much to his shock, Buffy confronts him and reveals that he blamed Billy for losing the game, and that he "caught up with him afterwards." At first, the Kiddy League Coach acted innocent and asked her what she was talking about, only for Billy to finally confront him. Billy confirmed Buffy was right, and that the Coach said it was Billy's fault that they lost. This prompted the Coach to try and flee the scene; however, he 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.