I am going to try some of the most popular Pokemon with a type advantage, and we can see how much each does. First, Landorus-T.
As you said, it is not a good counter at all. 252 Atk Landorus-Therian Earthquake vs. 252 HP / 28 Def Zacian-Crowned: 120-144 (60.3 - 72.3%) -- guaranteed 2HKO. This is the bulkiest set I found by the way. Anyways, zacian 2 hit KOs this thing anyways, and it's going to outspeed any day. With this set, Zacian still outspeeds. Zacian can then set up a swords dance, survive a hit, then outspeed and ohko. I would not use Landorus-T.
Groudon is not a good option either. Zacian outspeeds it, and can play rough twice to 2 hit ohko it. 252+ Atk Groudon Precipice Blades vs. 252 HP / 28 Def Zacian-Crowned: 162-192 (81.4 - 96.4%) -- guaranteed 2HKO. I am using the bulkiest set that I found for Zacian.
Next, lets look at Charizard. This thing can actually outspeed and do this much damage: 252 SpA Life Orb Charizard Heat Wave vs. 252 HP / 36 SpD Zacian-Crowned: 120-143 (60.3 - 71.8%) -- guaranteed 2HKO. It can also take a play rough quite well. I would say this is quite a good counter.
Next, we are at Torkoal. For torkoal, it will outspeed in trick room, which is where I believe it is usually run. 252+ SpA Charcoal Torkoal Eruption (150 BP) vs. 252 HP / 36 SpD Zacian-Crowned in Sun: 242-288 (121.6 - 144.7%) -- guaranteed OHKO. This is excellent. It surprisingly can also tank a close combat: +1 92+ Atk Zacian-Crowned Close Combat vs. 252 HP / 0 Def Torkoal: 94-111 (53.1 - 62.7%) -- guaranteed 2HKO. This is probably your best bet. However, I would like to go over some other options in case you don't like trick room.
Next, Coalossal. I am going under the assumption that the boost to the speed stat and the Special attack stat are already raised, because a max speed dragapult outspeeds the zacian set. This means that coalossal actually will outspeed zacian. +2 252+ SpA Coalossal Heat Wave vs. 252 HP / 36 SpD Zacian-Crowned: 168-198 (84.4 - 99.4%) -- guaranteed 2HKO. Unfortunately, this thing can't ohko, and Zacian gladly ohkos this thing.
Cinderace with max speed and jolly nature outspeeds zacian. This is amazing for it, as you never run it in trick room, but it also means that it has a very good chance to ohko, especially when you run life orb. 252 Atk Life Orb Cinderace Pyro Ball vs. 252 HP / 28 Def Zacian-Crowned: 213-252 (107 - 126.6%) -- guaranteed OHKO. Cinderace is another premier counter to zacian.
Overall, your best bets would be Torkoal or Cinderace. For reference, I tried out torkoal with a max special defense zacian and it still is a guaranteed OHKO. Cinderace has a 37.5 chance against a max defense zacian, but that is still quite good.
Hope this helped!