Just put Dr Manhattan inside The Phantom Zone, and throw away the key.

Except he'd have to get him in The Phantom Zone first... For all you know, Manhattan has multiplied so you're only locking away one of him.

Well, assuming that Doc actually pulled that off (despite never demonstrating himself to be remotely capable of teleporting another person that far) Superman would fly back to Earth is what.  Doc is limited to the potential of the laws of physics, Superman is not.  By flying FTL he is beyond Doc's ability to track.  Then he just punches the Doc's quantum state into something even more basic than quarks and the Doc has never shown himself to be able to reassemble from a sub-atomic state.  Fire up the phantom zone generator if he starts to.  Superman has flown billions of times the speed of light; he can easily assemble or prepare the device so that Doc doesn't have time to do anything to stop it.

"Superman is as strong as he needs to be."  Just imagine whatever feats are necessary to beat up Doc.  Superman is stated to be able to go beyond that.

The Superman downplay is real.

The Superman worship is bordering on the weird.

People are arguing he can beat a guy who can shape reality. He is part of reality.

Dude, Superman could punch him, but he would just fly straight through him, just like any other physical object you might throw at him.

Doc can see the past the current and the future all at the same time, he'd know that Supes would try, and would merely stop him. Also, just because Superman has (once) flown faster than the speed of light, does not mean other physical objects can react faster than the speed of light.

Why would Doc teleport the Phantom Zone gun thingy with Supes? He'd leave that on earth. And if Supes were to fly FTL back to earth (presuming Manhattan wouldn't be able to stop him) he couldn't just bring the Phantom Zone back with him while flying FTL. Any physical object (besides Superman because writers don't care) would disintegrate to a sub-atomic state if they went FTL, so suddenly, Supes' Phantom Zone gun would be nothing. And like I said, Doc would know exactly what supes was trying to do, and could react even before it would happen. Hell, he'd know before the fight would even start.

Also Supes has never been shown to be able to do fine tuning and use his fine motorics (like preparing and assembling the Phantom Zone gun) at FTL speeds.

When he has rebuilt himself from nothing, how can you say he can't rebuild himself from a sub-atomic state? He controls matter at a sub-atomic state, and he clearly exists outside of his mere physical form...

Is Superman made of matter? If yes, Manhattan can control him.

Heck, I could even argue that if you locked up Manhattan in the Phantom Zone, you would've only locked up his physical body, and since he clearly isn't tied to that, he would still be present and could just rebuild himself in this universe.

Your argument comes down to "Manhattan the omnisentient reality shaper with the powers of a God has never been shown to do exactly that, so obviously he can't do exactly that".

Superman has (repeatedly) gone FTL and used fine motor control at FTL.  Superman has repeatedly defeated reality warpers beyond what the Doc has been shown capable of.  The Doc is constrained by the limits of scientific laws and Superman is not.  Moreover, Superman has on multiple occasions bested and tanked effects by reality warpers who aren't as limited as the Doc.

Superman has shown this multiple times.  The feats you're claiming Doc is capable of are far beyond anything Doc has ever done.  Far beyond.

Superman is literally everything that Doctor Manhattan cannot understand.  The mere ability to go FTL, not to mention hear sounds in a vacuum light years away moments after the sound is made, would make Doc's head explode just trying to rationalize it.  From Doc's perspective, Superman is a god.  An impossible thing.  To Superman, Doc is just another opponent.  Dealing with him is just a matter of routine.  

Heck, Doc wouldn't even be able to use most of his abilities to their desired effect on Superman; Superman's quantum state passively denies Doc's method of manipulation by the very nature of his scientifically impossible superhuman durability.  Oh, and Superman has demonstrated this against reality warpers and magic users repeatedly as well.

Lol. "Dr. Manhattan is constrained by the limits of scientific laws" Ummmm...... Okee dokee. Doc is just as much an impossibility as Superman. I mean, the thing Supes did when he was at VEGA and heard the soound and travelled back to earth in 10 minutes or whatever, that's nothing compared to how the Doc would know about that fight before it happened. Just like he would know of Superman's every move before Superman even knew.

All I can think of reading this thread is 'How can people enjoy reading Superman?'

Then Doc would simply know that Superman's victory is inevitable.  He would forsee his own defeat and fatalistically accept it.  
And no, Doc's abilities are all rooted in physics.  Everything he does is based on strict mathematical formulae and every application of his powers are within their potential.  Superman breaks those formulae without giving a damn.  The Doc is a god in our universe, but he's not even a heavyweight in the DCU.