The Day the Music Died
Episode Synopsis: Jem agrees to get away from it all at the spur of the moment with Riot after a particularly stressful day. They subsequently get stranded on a tropical island together. In Jerrica's absence, Pizzazz and co. take over both the Holograms and the Stingers to create a supergroup Misfits. This is a particularly interesting episode as it's the only one narrated by characters in the story as it goes along. 

Rockin' Romance Jem
First appears in The Day the Music Died and again in: 

Riot's Hope.

Model sheet number Unknown
Hasbro did not produce this fashion. Well, they sort of did. Rockin' Romance Jem was available in extremely limited quantities, it is my assumption that the handful of dolls that have turned up were never mass produced or meant for wide distribution but rather samples and/or prototypes.
There are a few different prototypes known, but the few that were found in boxes have a much paler pink dress than the one that appears on the cartoon, with pearl drop earrings and necklace. The doll's hair is also not completely gathered in a pony tail but rather a section of hair has a ponytail; the hair is crimped. She comes with pink shoes and white tights with polkadots. In all versions I've seen so far (the boxed dolls + the catalogue photos), the skirt is not two layers of the same length, but rather has a small frill around the bodice and a longer skirt. She came with two zig zag white bracelets as opposed to one.
Integrity Toys produced this doll and fashion for San Diego Comic Con 2014.Integrity's version is much more like the cartoon, shown left. The main differences are that Integrity's version comes with dangle earrings, pink shoes and two bracelets rather than one.
Credits Thanks to tinkyjem for this drawing!
Island Getaway Jem
Makes its first and only appearance in The Day the Music Died.


Model sheet number Unknown
Hasbro did not produce this fashion.
Credits Thanks to Tffnynelson for this drawing!
Riot Swimsuit (with messy hair/seaweed)
Makes its first and only appearance in The Day the Music Died.

However the bathing suit design was also seen in The Stingers Hit Town Part 1, The Stingers Hit Town Part 2, The Day the Music Died, Change of Heart

Model sheet number Unknown
Hasbro did not produce this fashion.
Credits Thanks to sunnyday for donating this drawing to the wardrobe section!
Island Getaway Riot
Makes its first and only appearance in The Day the Music Died.


Model sheet number Unknown
Hasbro did not produce this fashion.
Credits Thanks to sunnyday for donating this drawing to the wardrobe section!
Riot Gold/Black Tux Riot
Makes its first and only appearance in The Day the Music Died.


Model sheet number Unknown
Hasbro did not produce this fashion.
Credits Thanks to sunnyday for donating this drawing to the wardrobe section!
"
Cruise Ship Jem
Makes its first and only appearance in The Day the Music Died.


Model sheet number Unknown
Hasbro did not produce this fashion.
CreditsThanks to sunnyday for donating this drawing to the wardrobe section!
Cruise Ship Riot
First appears in The Day the Music Died and again in: 

Riot's Hope, A Father Should Be....

Model sheet number Unknown
Credits Thanks to sunnyday for donating this drawing to the wardrobe section!
Jem Swimwear (Blue)
Makes its first and only appearance in The Day the Music Died.

This swimsuit has been shown before and since, in shades of pink.

Model sheet number Unknown. 
Notes *I'm guessing on the shoe style/colour.

Also featured in this episode (debuted earlier in the series) are the following fashions, not including recaps. 

"Bad" Kimber (purple net dress) Raya Turquoise/hot pink/orange Aja Sharp, Not Flat Shana Star studded fashion Jerrica Red/White pantsuit Rio Green shirt/brown suede jacket Kimber Shirt & Tie Pantsuit
Raya Garden Party 24 Carat Sound Broadway Magic (Jem) (Without the cape) Love's Not Easy Pizzazz Animal Print Dress/jacket Wicked Sister Raya Riot Stage Fashion
Rapture Stage Fashion Minx Stage Fashion Roxy "Jack Take a Hike" Wicked Sister Aja Wicked Sister Shana Minx Red Pillbox Hat Fashion Rapture Tiger Striped Pants fashion
There Ain't Nobody Better Roxy Rock Fashion Book Jetta Yellow/Green Ruffle Dress Kimber "Something is Missing" Pantsuit Aja white pants/coral top Roxy original outfit (Revised) Stormer Original Outfit
Jetta Original Outfit Raya Original (Doll) outfit Kimber Original Outfit Aja Original Outfit Shana Original Outfit Pizzazz "dyed black" pantsuit Kimber purple spiral dress
Gimme Gimme Gimme Aja Pink Chinese Power Suit Shana Green triangle dress suit We're Off and Running You Can't Catch Me Jetta Purple/black/white ponytail outfit Raya "Jazz Has"
Designing Woman You Gotta Be Fast Just Misbehavin' Princess Adriana Outfit Jem Casual Hawaiian outfit Riot Bathing Suit Minx Star Skirt Fashion
Rapture Striped Tube Top Rio Khakis Kimber Aztec Khakis Aja Khakis Raya Summer Shorts suit Shana Army Jacket Shorts set Jetta yellow ochre blazer outfit
Outta My Way (green) Roxy Magenta/Yellow minidress Jerrica Trip to the Zoo Hollywood Jem American Beauty Jem Rock 'n Roses Set Your Sails
She Makes an Impression (Jem) Raya Purple Star Halter Dress Jem Maid of Honor Dress There's a Melody Playing We Can Change it (Jem)

Back To Jem Episode 59: Midsummer Night's Madness

On To Jem Episode 61: That Old Houdini Magic