While I generally shy away from songs and kids music that explicitly teach subjects in a didactic way, that doesn't mean that a) non-didactic songs don't teach the listener, and b) you can't create a very catchy song that also happens to be educational.
There are lots of songs that take history as their subject, and there are any number of math, non-English language, science, and standard school or preschool life skill subjects in song. Emotional literacy, however, is a trickier subject, as the songwriter isn't so much covering facts as she or he is trying to write a song explaining the very emotions songs usually generate. It's a meta idea... for 4- or 7-year-olds.
Back in 2008, I said that there really hadn't been much if any non-didactic kids music about emotions written, and that there was a niche waiting to be filled. Luckily, I think that niche has been filled, at least a little bit -- there are now a number of tracks that I think could serve as tuneful introductions for a young audience to what emotions are.
I've provided a list below, but if you've got more to add, list them in the comments! (Note that the list generally tries to limit itself to songs about emotion, rather than including songs that deal with emotion in passing. Such a list would be much, much longer.)
“It’s Alright to Cry” - Rosie Grier (among many others) [stream]
"Cry Cry Cry” - Ziggy Marley (feat. Jack Johnson & Paula Fuga) [stream]
“Joy Comes Back” - Alastair Moock [stream]
“Furry Happy Monsters” - R.E.M. [video]
“Sad” - Big Block Singsong [video]
“Brave” - Big Block Singsong [video]
“Happy” - Big Block Singsong [video]
"Mad" - Big Block Singsong [video]
“Mama Is Sad” - Justin Roberts [stream]
“Happy Sad Silly Mad” - Jeremy Plays Guitar [video]
“Sad Robot” - The Jellydots [stream]
“Are You Happy?” - Alison Faith Levy [stream]
“If You’re Happy and You Know It..." - Raffi (and many many others) [stream]
"In All of the World" - Papa Crow [stream]
"Alright, Okay, Just Fine" - Gwendolyn and the Good Time Gang [Spotify]
"Feel What U Feel" - Lisa Loeb feat. Craig Robinson [Amazon]
"Feelings Change" - The Pop Ups [stream]