I always seem to get late for these posts!
Like mentioned, good and evil are relative when applied to perspective. If you humanize characters, if you give them dimensions, then they won't be ''evil conquerors'', they'll be complex creatures with motivations we can understand. I feel like that's the way to go.
That said, this is a pretty interesting topic, because conquest is, indeed, a pretty universally accepted ''evil act''. I feel like any conqueror is already a ''grey'' character, so if you don't mind your protagonists having some shades of complicated morality to them...
A Conqueror is, by definition, someone that conquers, which implies taking land and pushing a certain worldview to people. We can, of course, imagine conquerors that don't do that, who don't push cultures, how could that work? Would that make them less evil? In a way, one can look at USA's old tactic of tearing down old regimes and establishing new rulers more inclined to their tastes as a more subtle, modern kind of conquest, all in the name of ''freedom''. A conqueror is someone with a least a bit of ego, someone who thinks they can do better, that they know better. Or, as you said, in fiction they might just be so damn bored.
Diego mentioned a good trope that describes this, the ''Well-Intentioned extremist''. We all know TV Tropes is not like a writer's bible or anything, but it's always good fun, so you might look for the page!
Have you ever played Final Fantasy Tactics? Delita is not a conqueror, he's a man trying to socially rise until he makes it to king, but he's a pretty good character of the kind. He's an extremist and a terribly corrupt character, but one that does what he does for ''the people'' (and, as always with these types, for himself too) and it's hard not to empathize with the little jerk. I mean, Tactics is just plain good writing.
I'd also recommend some Marvel, mainly modern runs by Jonathan Hickman and the amaaazing Ta-Neshi Coates Black Panther run. It's said that Marvel can be read as a universe of men trying to be gods.
Hickman wrote New Avengers about the Illuminati, a group of kings and leaders of men (people like Iron Man, Black Panther, Black Bolt, Namor...) that face an impossible situation. They're ''heroes''. We understand, love and pity them, but we also see the fault in them. What kind of men would think so high of themselves as to appoint themselves rulers? What's the moral toll? So they're not evil, but they're flawed.
In the same run, Hickman writes an awesome Doctor Doom, which is THE noble monarch villain to me. Latveria, his country, actually likes him. He's a good king. I mean, look at this panel:
Hickman even gives Doom the chance to do serious good in his follow up Secret Wars and he basically becomes THE CONQUEROR. Still, there are flaws within himself. Doom is a bad man who can do good. He's complex. He's ''evil'', but we can cheer for him.
(I mean, please everyone, give Hickman's Fantastic Four/Avengers/New Avengers/Secret Wars massive opus a chance someday!!!)
Just to finish this looong ass post, Ta-Neshi Coates first story arc for Black Panther was about the failings of keeping Wakanda as a monarchy in modern times. T'Challa is a great character and those two comics milk him for all he's worth, his most noble and his most morally compromised. It's another great look into a cool king kind of character and the limits of it.
Can we make this an inside joke, please? Everyone putting this sentence in their story at some point or another!
