The very first episode could sometimes be a bit narmmy but was mostly very heartwarming.
"Alamo Jobe" had the heartwarmingly dedicated messenger Jobe. He learned the fate of the Alamo and instead of staying in the future where he'd be safe, he went back to the battle. Also a Tear Jerker episode.
The fading illusionist from "Mr. Magic" gets one last shot at greatness thanks to a deck of magic playing cards. The Tear Jerker part comes at his "last" show, when he announces that he is going to retire. He leaves the stage, then the cards fly out and form the word "Goodbye." They then fly back into his hand. Awwwww.
Major overlap with Tear Jerker is in "The Mission." As a World War II plane prepares to land, its landing gear damaged, their "lucky charm" belly gunner trapped in the bottom of the plane, the rest of the crew goes to him one at a time to rub his head and say goodbye. You can watch the episode a hundred times, know exactly how it's going to turn out, and still blubber like a baby.