I made a list by Stardate order just for the fun of it and next revisit I'm going to try it this way. For the hell of it I also included TAS episodes (listed in bold type), but the oddity is that "The Magicks Of Megas-Tu has an earlier Stardate than "Where No Man Has Gone Before." Wierd. I might shunt that one to the end.
As for the five TOS episodes with no Stardate. I started with a list of production order and then moved the episodes accordingly. As such I left the no-stardate episodes where they were.
“The Cage”
“The Magicks Of Megas-Tu”
“Where No Man Has Gone Before”
“Mudd’s Women”
“The Corbomite Maneuver”
“The Man Trap”
“Charlie X”
“The Enemy Within”
“The Naked Time”
“Balance Of Terror”
“The Squire Of Gothos”
“Patterns Of Force”
“What Are Little Girls Made Of?”
“Miri”
“Dagger Of The Mind”
“The Conscience Of The King”
“The Galileo Seven”
“Courtmartial”
“The Menagerie”
“Catspaw”
“Shoreleave”
“Arena”
“The Alternative Factor”
“Tomorrow Is Yesterday”
“The City On The Edge Of Forever”
“Space Seed”
“The Return Of The Archons”
“The Practical Joker”
“A Taste Of Armageddon”
“The Devil In The Dark”
“Errand Of Mercy”
“The Gamesters Of Triskelion”
“Metamorphosis”
“Operation--Annihilate”
“Amok Time”
“This Side Of Paradise”
“Who Mourns For Adonais?”
“The Deadly Years”
“Friday’s Child”
“The Changeling”
“Wolf In The Fold”
“Obsession”
“The Apple”
“Journey To Babel”
“Bread And Circuses”
“Slaver Weapon”
“The Doomsday Machine”
“Mirror, Mirror”
“A Private Little War”
“The Immunity Syndrome”
“Elaan Of Troyius”
“Spectre Of The Gun”
“I, Mudd”
“The Trouble With Tribbles”
“A Piece Of The Action”
“By Any Other Name”
“The Ultimate Computer”
“Return To Tomorrow”
“The Omega Glory”
“Assignment: Earth”
“The Paradise Syndrome”
“Mudd’s Passion”
“And The Children Shall Lead”
“The Enterprise Incident”
“The Empath”
“The Survivor”
“Time Trap”
“Albatross”
“One Of Our Planets Is Missing”
“Yesteryear”
“More Tribbles, More Troubles”
“The Mark Of Gideon”
“Spock’s Brain”
“For The World Is Hollow And I Have Touched The Sky”
“The Lorelei Signal”
“The Ambergris Element”
“Eye Of The Beholder”
“Beyond The Farthest Star”
“The Infinite Vulcan”
“The Terratin Incident”
“Once Upon A Planet”
“Is There In Truth No Beauty?”
“Jihad”
“The Tholian Web”
“Day Of The Dove”
“Wink Of An Eye”
“Whom Gods Destroy”
“The Lights Of Zetar”
“Let That Be Your Last Battlefield”
“Plato’s Stepchildren”
“That Which Survives”
“The Cloud Minders”
“The Way To Eden”
“Requiem For Methuselah”
“The Savage Curtain”
“Turnabout Intruder”
“All Our Yesterdays”
“How Sharper Than A Serpents Tooth”
“The Pirates Of Orion”
“The Counter-Clock Incident”
“BEM”
As for the five TOS episodes with no Stardate. I started with a list of production order and then moved the episodes accordingly. As such I left the no-stardate episodes where they were.
“The Cage”
“The Magicks Of Megas-Tu”
“Where No Man Has Gone Before”
“Mudd’s Women”
“The Corbomite Maneuver”
“The Man Trap”
“Charlie X”
“The Enemy Within”
“The Naked Time”
“Balance Of Terror”
“The Squire Of Gothos”
“Patterns Of Force”
“What Are Little Girls Made Of?”
“Miri”
“Dagger Of The Mind”
“The Conscience Of The King”
“The Galileo Seven”
“Courtmartial”
“The Menagerie”
“Catspaw”
“Shoreleave”
“Arena”
“The Alternative Factor”
“Tomorrow Is Yesterday”
“The City On The Edge Of Forever”
“Space Seed”
“The Return Of The Archons”
“The Practical Joker”
“A Taste Of Armageddon”
“The Devil In The Dark”
“Errand Of Mercy”
“The Gamesters Of Triskelion”
“Metamorphosis”
“Operation--Annihilate”
“Amok Time”
“This Side Of Paradise”
“Who Mourns For Adonais?”
“The Deadly Years”
“Friday’s Child”
“The Changeling”
“Wolf In The Fold”
“Obsession”
“The Apple”
“Journey To Babel”
“Bread And Circuses”
“Slaver Weapon”
“The Doomsday Machine”
“Mirror, Mirror”
“A Private Little War”
“The Immunity Syndrome”
“Elaan Of Troyius”
“Spectre Of The Gun”
“I, Mudd”
“The Trouble With Tribbles”
“A Piece Of The Action”
“By Any Other Name”
“The Ultimate Computer”
“Return To Tomorrow”
“The Omega Glory”
“Assignment: Earth”
“The Paradise Syndrome”
“Mudd’s Passion”
“And The Children Shall Lead”
“The Enterprise Incident”
“The Empath”
“The Survivor”
“Time Trap”
“Albatross”
“One Of Our Planets Is Missing”
“Yesteryear”
“More Tribbles, More Troubles”
“The Mark Of Gideon”
“Spock’s Brain”
“For The World Is Hollow And I Have Touched The Sky”
“The Lorelei Signal”
“The Ambergris Element”
“Eye Of The Beholder”
“Beyond The Farthest Star”
“The Infinite Vulcan”
“The Terratin Incident”
“Once Upon A Planet”
“Is There In Truth No Beauty?”
“Jihad”
“The Tholian Web”
“Day Of The Dove”
“Wink Of An Eye”
“Whom Gods Destroy”
“The Lights Of Zetar”
“Let That Be Your Last Battlefield”
“Plato’s Stepchildren”
“That Which Survives”
“The Cloud Minders”
“The Way To Eden”
“Requiem For Methuselah”
“The Savage Curtain”
“Turnabout Intruder”
“All Our Yesterdays”
“How Sharper Than A Serpents Tooth”
“The Pirates Of Orion”
“The Counter-Clock Incident”
“BEM”