tank with least buttons for 4 mans

[Thela]

DRK will run out of mp faster than PLD will run out of TP.

PLD just spams TE / Flash and alternate when their run out of one type of resource. 2 buttons.

WAR will spam OP but needs do to SE combo to maintain buff and potentially do Cyclone. 4-5 buttons.

DRK will spam AD and Unleash but will need to replenish mp with SE and potentially TBN for quietus. You're looking at 5-7 buttons.

So no, the correct answer is PLD.

But nobody asked which tank is better/easier or whatever to play, the question was which tank has the least amount of buttons and the answer to that question is most definitely NOT Paladin.

And if you just spam TE / Flash and nothing else you're really not gonna get very far, just saying. If you go by that logic then the correct answer would be Warrior, doing nothing but Overpower which will create enough aggro for you to just stand there after you run out of TP waiting for it to replenish. Or indeed Paladin doing nothing but Flash. But I'm assuming the OP want to play the job CORRECTLY.

[Shinkyo]

But nobody asked which tank is better/easier or whatever to play, the question was which tank has the least amount of buttons and the answer to that question is most definitely NOT Paladin.

The question in the title is from my understanding "which tank requires the least button to run 4-man content (i.e. dungeons)?" so I'm simply answering in that mindset.

Flash/TE is the correct way to play PLD in dungeon big pulls until you reached a boss.
Only when you've burned the mobs down to 3, you may want to Goring if it's gonna tick in full.

All I'm saying is that with a minimum of 2 buttons and on trash mobs, PLD is more efficient than the WAR/DRK. It's less potency per GCD but it's more sustainable and you're not playing it wrong.
But really the OP question is a bit weird in the first place :-)