So I've spent many hours exploring this very thing and her it is:
Soraka: Spirit Visage Warmogs into counter resistant items depending on who you face. Forget about W, max Q to be annoying and E to tell anyone NO in prolong fights. Take this top and be on the floor laughing.
Karma: Maxing her shield on top of counter tank objects can be increditable since you can use your ult at lvl 1 and get a huge shield without building any shield/healing objects or even ap items.
Janna: The same Reasons as Karma
Bard: Chimes will give you any and all the power you need. Ult to pause fights and engage. magical journey I love to max out to always have a escape power on top of that I build nothing but HP+armor or HP+magic resist. Taking all of that and building Predator will help you run away from anyone. I once out ran a hec and a yi by using my Magical Journey stuning them to each other when they continued to chase and then as they were stunned i popped Predator and ran off. Also any dmg they did to me before the journey was very little as i build enough armor and magic resist with HP.
Teemo: Never did it but I've seen it, and its funny. Keep in mind Demolish will scale heavily with hp amounts so you can still split push without dmg.
Morgana: Max your Spell Shield then your Snare the pool as a tank will be a waste of mana. She will be the counter to all kinds of tops that have cc or magic dmg.
Kayle: I mean Ult gives her invul paired with gargoyles i mean it could work well, morgana i feel could be better but still.
Zyra: Max your Seeds and build counter Resist items, both your 1-14 plants and yourself will be very tanky by mid-late game and very annoying to be around.
ZILEAN: Can i say more? lol that slow/speed up, his ult, and if you use Quick cast on his Q his stun becomes a bit easier at times. ZZrots is OP and helpful on tanks.
Ashe: SLOWSSSSSSS grab Glacial Augmentation and build tank. Laugh at your foes as they never walk fast again.
R_A_K_A_N: this one should be obvious but everyone prefers dmg or healing so I'll count it. Just stand around in areas they can poke you at and right before the poke happens dash away with his knock up dash, or if an ally is close by use his shield to evade it. You are a tank Rakan so messing this up won't 1shot you.
Veigar: I know you said no power, and there will not be any unless you are getting tons of cs and pokes off. If you build tank and there are full ap mages/assassins/supports/bottoms/jungles/tops then this will use all their ap against them while you remain tanky from all the tank items.
Shaco: Clone is Tanky, you are Tanky, Boxes will be annoying AF and shiv will provide a great slow.
Kennen: Stufff... Words, Explanation... (I have to many fun ideas.... I'll let you figure this one out on your own)
Anivia: All her cc plus being only with tank items can be annoying, also please note, EGGNIVIA WILL BE TANKY TOO
Fiddlesticks: when maxing out his fear it can last up to 2-4 seconds long!!
Ivern: Build Tank, and when they leave lane from boredom take a control ward and a scaning lens into their jungle and steal everything to become even more tanky.
Azir: When he collides with someone he gets a shield, and if you can dash behind them or at them and then move/flash behind and ult them at the allies it will be splendid engage while remaining tanky from all those tank items.
Orianna: Maxing shield and her slow will help with the CC department and the ult tips the scales if you are tanky on top of this it will make your robotic body seem actually made of some metallic material.
ANNIE: Maxing her DMG REDUCTION fire circle shield and going tanky will make you a pain to kill just remember out side that stun, and bear you will be a meat shield.
I'm done now, this took 10mins of fun memory lane jogging but it was fun none the less. I hope this helps you out in finding something annoying and tanky to play.