With all that as a caveat, here is what I have determined to be the best guesstimate for most requested songs in the show's history.
#100 The Hamilton Polka - "Weird Al" Yankovic
#99 Save Me, Obama - Robert Lund
#98 Great Idea For A Song - Worm Quartet [tie]
#97 Second Week Of Deer Camp - Da Yoopers [tie]
#96 Peed In My Pants - Knuckleheadz
#95 Boogie In Your Butt - Eddie Murphy
#94 C. B. Savage - Rod Hart
#93 Always Look On The Bright Side Of Life - Monty Python
#92 Science Geek - The Amoeba People
#91 Carrot Juice Is Murder - The Arrogant Worms
#90 Gilligan's Island (Stairway) - Little Roger & The Goosebumps
#89 The Ballad Of Ben Gay - Ben Gay & The Silly Savages
#88 Polka Dot Undies - Bowser & Blue
#87 My Ding-A-Ling - Chuck Berry
#86 Junk Food Junkie - Larry Groce
#85 Monster Hash - The Toyes
#84 Ice Box Man - George Carlin
#83 Marvin I Love You - Marvin The Paranoid Android
#82 Werecow - Flippy T. Fishead & The Mighty Ground Beeves
#81 When You Wish Upon A Death Star - the great Luke Ski [tie]
#80 Fake Adult - the great Luke Ski [tie]
#79 Psycho Chicken (Clucked) - The Fools [tie]
#78 Bras On 45 - Ivor Biggun & The D. Kups
#77 99 Dead Baboons - Tim Cavanagh
#76 Ode To My Car (Car Honk Version) - Adam Sandler
#75 Polkamania! - "Weird Al" Yankovic [tie]
#74 Benedict Cumberbatch - Insane Ian [tie]
#73 Snoopy The Dogg - the great Luke Ski [tie]
#72 Big Bruce - Steve Greenberg
#71 Grandma Got Run Over By A Reindeer - Elmo & Patsy
#70 Transfusion - Nervous Norvus
#69 The Chainsaw Juggler - The Four Postmen
#68 White & Nerdy - "Weird Al" Yankovic
#67 Frosty The Dopeman - Marc Zydiak
#66 Rock And Roll Doctor - Travesty, Ltd.
#65 One More Minute - "Weird Al" Yankovic
#64 Eat It - "Weird Al" Yankovic
#63 Mwahaha - Ookla the Mok
#62 My Name Is Larry - Wild Man Fischer
#61 Moose Turd Pie - Utah Phillips
#60 Ricky - Wolves Of Glendale
#59 Da Turdy Point Buck - Bananas at Large
#58 I Made It With A Bagel And Cream Cheese - SuLu
#57 Hooray For Captain Spaulding - Groucho Marx
#56 The Night Santa Went Crazy - "Weird Al" Yankovic
#55 Lumberjack Song - Monty Python
#54 Making Love In A Subaru - Damaskas
#53 Bounce Your Boobies - Rusty Warren
#52 The Ultimate Showdown Of Ultimate Destiny - Lemon Demon
#51 Titties And Beer - Frank Zappa
#50 The Ballad Of Bilbo Baggins - Leonard Nimoy
#49 Institutionalized - Brak
#48 Christmas at Ground Zero - "Weird Al" Yankovic
#47 The Saga Begins - "Weird Al" Yankovic
#46 The Masochism Tango - Tom Lehrer
#45 Let's Blow Up The Tow Truck - Krypton
#44 I've Got No More F'S To Give - Thomas Benjamin Wild, Esq.
#43 After Ever After - Jon Cozart [7]
#42 My Dead Dog Rover - Hank, Stu, Dave & Hank
#41 The Time Warp - The Rocky Horror Picture Show Cast
#40 I Like - Heathen Dan
#39 Sahra Cynthia Sylvia Stout Would Not Take The Garbage Out - Shel Silverstein
#38 Viagra In The Waters - Camille West/The Four Bitchin' Babes [6]
#37 It's A Gas - Alfred E. Neuman
#36 Friendly Neighborhood Narco Agent - Jef Jaisun
#35 Deteriorata - National Lampoon
#34 Earache My Eye Featuring Alice Bowie - Cheech & Chong
#33 The Devil Went To Jamaica - Travis Meyer
#32 Spam - Monty Python
#31 The Vatican Rag - Tom Lehrer
#30 Monster Mash - Bobby (Boris) Pickett & The Crypt-Kickers
#29 The Cockroach That Ate Cincinnati - Rose & The Arrangement
#28 Homecoming Queen's Got A Gun - Julie Brown
#27 Amish Paradise - "Weird Al" Yankovic
#26 Cows With Guns - Dana Lyons
#25 Last Will And Temperament - The Frantics
#24 Dungeons And Dragons - The Dead Alewives [5]
#23 Squirrels - The Beastly Boys
#22 Who's On First - Abbott & Costello
#21 Poisoning Pigeons In The Park - Tom Lehrer
#20 Boobs A Lot - The Holy Modal Rounders/The Fugs [4]
#19 Kinko The Clown - The Ogden Edsl Wahalia Blues Ensemble Mondo Bizzario Band
#18 Pico And Sepulveda (The Street Song) - Felix Figueroa & His Orchestra [3]
#17 Another One Rides the Bus - "Weird Al" Yankovic
#16 The Scotsman - Bryan Bowers
#15 Stardrek - Bobby Pickett & Peter Ferrara
#14 Star Trekkin' - The Firm
#13 Hello Mudduh, Hello Fadduh! (A Letter From Camp) - Allan Sherman [2]
#12 Bulbous Bouffant - Radio Free Vestibule
#11 The Smoke-Off - Shel Silverstein
#10 The Ballad Of Irving - Frank Gallop
#9 Yoda - "Weird Al" Yankovic
#8 Ti Kwan Leep/Boot to the Head - The Frantics
#7 Wet Dream - Kip Addotta
#6 Pencil Neck Geek - Fred Blassie
#5 Existential Blues - Tom "T-Bone" Stankus
#4 Shaving Cream - Benny Bell/Dr. Demento/Fabulous Five Inc. [1]
#3 They're Coming To Take Me Away, Ha-Haaa! - Napoleon XIV
#2 Dead Puppies - Ogden Edsl Wahalia Blues Ensemble Mondo Bizzario Band
#1 Fish Heads - Barnes & Barnes
How I break ties:
1. number of times on chart
2. highest peak position
3. number of times at peak position
4. number of non-charted plays
[1] "Shaving Cream"'s position includes all 3 charted versions: Benny Bell (Vocal: Paul Wynn), Dr. Demento (all versions), and Fabulous Five Inc. Counted separately, the Benny Bell/Paul Wynn version would've been at #8 and the Dr. Demento version would've been at #19.
[2] "Hello Muddah..." combines points from when the original version appeared on the countdown and when the "New 1964 Version" appeared. This is because the two were often counted together in the 1970s to determine its position, and sometimes one or the other or both were played.
[3] "Pico And Sepulveda" was removed from competition after November 26, 1972, due to appearing at #1 too often and wanting to give others a chance. A rough estimate of the points it would have obtained had it not been exempted was used to determine its ranking.
[4] Points from the Fugs version of "Boobs A Lot" were added to the Holy Modal Rounders total, although this did not change its position in the countdown.
[5] Points from "Dungeons And Dragons II" were combined with the original, but this did not affect its position in the countdown.
[6] Points from the Four Bitchin' Babes version of "Viagra In The Waters" were combined with Camille West's version to determine its ranking. If not combined, Camille's version would've been #40.
[7] Points for "After Ever After 2" were combined with "After Ever After" to determine its ranking, in the same spirit as "Hello Muddah..." above, but this may have been the wrong tactic here. If counted separately, "After Ever After" would be at #68 and the follow-up would not be in the top 100.