Throughout the hunter series, there are people who are speculated to be god-class in power. Meruem himself is of course one such being. Alluka is another obvious example. I can list a few others in this category to give you a gist. In my view, only with power of such a class can one defeat the ant king.
Don Freecs (the grandfather of Ging) is one character who can be ascribed such a power level. He is strong enough to live in the dark continent permanently; constantly charting and mapping the area and writing books about the species and wonders found there. Mind you, the dark continent is where the chimera ants originate from. The continent contains creatures so deadly that they make the chimera ants seem like insignificant mere miniature ants by comparison; thus for a nen user to be powerful enough to choose to dwell there, then he must be a good contender to fight and defeat Meruem.
Kite's new identity as Meruem's sister, gives her the immense nen capabilities of a chimera ant Princess, effectively placing him in the god class category capable of fighting an ant king.
Eventhough it is unconfirmed, there is reason to believe that the sonata of darkness which deformed Melody, was not written by the devil himself but was in fact written by a nen user whose power is so vile that it could easily be referred to as devilish. A being of such power could also be a good contender against Meruem.
If anyone of Netero's power level (for instance, anyone in the legendary seirin group) uses a nen restriction (ie: takes a leaf from Gon's book) during battle, that individual should then be powerful enough to defeat the ant king.
Maha Zoldyck in his prime was an assassin like we have never seen before. There was almost no method of death dealing in the grim reaper's arsenal that Maha could not dish out. He would be the only guy I would tip to be capable of 'dwelling successfully' in the dark continent (aside Don Freecs of course); indeed, "god-class" was not out of his purview. However, given that Netero 'survived' a battle with Maha, the ant king would most likely survive him too. They could be equal in combat, but I doubt Maha could dish out a true defeat.
There are abilities in the hunter universe that could instantly make one a god-level combatant. In fact, I believe Killua even mentioned one in the greed island arc when he stated that the combination of risky dice and fickle genie could make an individual quite powerful. It would be akin, or the same effect as someone who wished for Alluka to grant them a power/ability/strength capable of defeating the ant king.