I'm bored. So Sure.

These I keep seperate because they are primarily played in support. Other tanks have been played in support, but for the purpose of this discussion we'll use their intended roles of Top, mid, and jungle (Blitzcrank is an interesting case because he was actually originally built for top, but multiple seasons of supporting have thrust him into the support lane for what his kit offers).

Now one thing you should notice about all of these champions is that tank is their primary role. Their secondary role doesn't really matter much at all in classification (there are exceptions of course. But exceptions are not the rule. If that were the case,
would be considered an assassin).
But there is more to it than just that. Each of these champions has some form of CC or built in peel mechanism.
has his headbutt and knock up.
has his slow, stun passive, and knock up ult.
has two stuns.
root and knock up.
and
have taunts on top of effects that benefit allies defensively.
has a wall stun, an anti dash field, and a disengage ult that can be used offensively.
I'm not going to describe every champions ability, that will make this more of a text wall.
No I'll show you what shows up when you choose tanks in the shop rather than look at their primary search in the champions filter on your profile in the client (because the client still has some old functions and (as you pointed out) Riot has not actually input the new classes and subclasses into the client. This does not mean that they are not to be used.).

Now these champions have tank as their secondary. Meaning they have some aspects of a tank, but not enough to actually allow them to be a proper tank for a team. Their are at best, meatshields that provide huge damage. Because that is what their kits are built for, dealing damage and surviving fights.
Tank kits are not designed to deal fighter (which is what those champions primarily are) level damage. Tanks can do damage, but only enough to make glass cannons afraid of them. These fighters do not have the same level of utility as actual tanks. Mundo just has a slow. Darius has a hook with a short range. Nasus has a slow, and it's a damn powerful one, but he can only hit one target, which is mainly so that when he's at a massive number of stacks, he can kill that target by preventing them to run away.
There are obvious outliers, as Riot pointed out there would be in the subclasses.
for example was originally a juggernaut, but Riot plans on switching him to the vanguard class due to how his kit actually works.
is primarily a tank, but has such a weird kit that I can't imagine him really fitting into the role. Especially how he's a primarily split push champion and tanks are more teamfight focused. I guess you could call him a split push juggernaut.
is primarily a tank, but his numbers have been changed so much that he's either played as a full AD assassin or a form of bruiser. So I'm not sure I can consider him to be one. I'll be fine if I am wrong though.
Interesting tidbit: Tanks can build like fighters and fighters can build like tanks. They use very similar items (mainly the health part). It's just that many tanks do not actually function as well as fighters when building like a fighter, and vice versa (though of course people will still call tanks broken if
has no AD items yet one hit kills the villain with his ult while the villain is low).
was an AP bruiser, but his utility has made him into more of a tank in the recent years and will probably be labeled as such.
has become a knock up bot. I don't know what Riot plans for her.
: I personally don't think he's in his mega form enough to count as a tank, but that's what Riot calls him.
Though if you didn't want to read all of this or still have doubts as to what Riot considers a tank. Please read the following link.
http://boards.na.leagueoflegends.com/en/c/developer-corner/3A5uuBw7-champion-subclass-list
Now, Tanks that can utilize Black Cleaver are as follows:
and (if you consider him a tank)
.
Tanks that Black Cleaver is both core and very much viable on are as follows:
and (again, if you consider him a tank)
.
Please tell me what you consider a tank is and why. And if you're reasoning is, "because they are tanky" then please know that I have heard that answer hundreds of times. It is not what makes a tank a tank, not alone.