I've only seen about 30% of the episodes in some form and I've been busy to some extent lately, but I've found at least a few heartwarming moments from the series (in no particular order)...

1. Season 7, Episode 7, near the end of the episode: Frank and Laverne's father-daughter dance.

2. Season 3, Episode 18, end of the episode: "Milwaukee Moon" song

3. Season 2, Episode 16, near the end of the episode: Frank offering a temporary job at the Pizza Hall for both Laverne and Shirley and then having a dance with them at the taxi dance hall.

4. Season 8, Episode 3, near the end of the episode: Laverne finding the rest of Shirley's letter and reading it out to the group.

5. Season 2, Episode 9, near the end of the episode: Laverne and Shirley comforting Lenny and Squiggy after tracking them to the traveling circus and after learning Lenny and Squiggy will not be accompanying the circus.

There are many other such moments throughout the series.