Enough of pretty much anything can hurt him, at least post-Crisis. Big jolts of electricity seem relatively effective, at least at causing him pain and stunning him a bit, and energy weapons can mark him. It takes a lot to do him any significant harm, though. He’s also at least somewhat vulnerable to psychic assaults. Trapping him in a dream seems popular. That might incapacitate him long enough to come up with something.
If you’re looking to kill him without resorting to kryptonite or red sunlight, your best shot is probably asphyxiation. He has to breathe (again, post-Crisis). It would be tricky, of course–his invulnerability protects him from decompression, and he can probably hold his breath for a long time, so you would have to be able to keep him in an oxygen-free environment for a significant period.
If you’ve got space-capability, you could deploy a decoy ship with a phony distress signal at least a few light-minutes from the nearest breathable atmosphere. Rig a self-destruct for the ship that will wreck whatever he’s using for life support–a suit, or just a mask and oxygen tanks, will be far more fragile than he is. When he takes the bait, blow the ship and leave him stranded too far out to reach air before he loses consciousness.
If you’re not Lex Luthor, or Batman in contingency mode, and are constrained by your resources, you might try an old-fashioned moral-dilemma deathtrap. Set up an airtight structure in the middle of a public and densely populated place and lure him into investigating it. Seal it on him and flush it with a mix of argon and nerve gas. If he breaks out, it will flood the area with the nerve gas, killing large numbers of innocent people. Then you hope he doesn’t figure out a way to escape without releasing the gas before he passes out. It’s dicey, of course–heroes get out of stuff like that all the time–but it is a way that a non-powered individual with realistic (though substantial) resources could at least make the attempt.
Generally, I would expect direct applications of magic to bypass his invulnerability, while evoked effects (fireballs, lightning, and so forth) would affect him more-or-less like natural versions of those phenomena. So hitting him with a fireball would be roughly as effective as using a flamethrower on him–i.e., it would annoy him and possibly interfere with his vision a bit. A spell to turn him into an aardvark, on the other hand, would probably work…though it might leave you with a super-strong, invulnerable aardvark.
Unfortunately, the writers have been nowhere near that logical.