Challenge him to a children's card game and send him to the Shadow Realm.
...this sounds like a joking answer, but with the proper hostage situation, he'd be forced to play along, and would summarily have his soul trapped forever, presuming he lost. There has been precedent for his ability to escape from alternate dimensions - Superboy Prime notably punched out of more than a couple - but these have required him to have physical mass, and separating his soul from his body would, well. There you go.
Of course this approach runs into a couple of problems.
The first is that you need to actually
beat him in the card game, but this is easily solved by forcing him to play along with a pre-stacked deck, one specifically stacked against him.
The second is the inherent need to crossover with a different multiverse to gain access to Shadow Games and Yugioh magic, which is a
much more significant hurdle - but really, once you're seriously considering the idea of killing
freaking Superman, I say pull out all the stops. Worse comes to worst, DC Earth is a supremely magic-rich environment; I'm sure there's a knockoff of some sort hiding somewhere in some forbidden archive or another.
The third problem is the Flash's Speed Force, which could hypothetically let him vibrate to the dimensional frequency of the Shadow Realm and rescue Superman's soul, but this is solved by ... well, it's solved with difficulty. The most basic answer is "keep the card game a secret", but let's face - keeping a secret from the entire Justice League is more than a little difficult. But here's what's important: it's
not impossible.
Basically, what I'm trying to say is, the proper application of children's card games lets you punch
way above your weight class.
