The Sith always betray one another. Vader would have to have found a suitable apprentice, soemthing of the "Savage Opress" variety. A violent, powerful monster that would be able to take the full force of Palpatine and keep going. Palpatine was too powerful for Vader alone. He may have been the chosen one, but he was still not powerful enough, and definately not smart enough to defeat Palpatine. Especially since Palaptine doesn't actually "die" until all the clones of his own body are destroyed, and he can no longer keep moving himself within the force from one body to another younger one. Vader couldn't have known this.
One way or another, Vader would have tried to overthrow his old master. There is no way around it. Every Sith in history has been betrayed and destroyed, only to have their apprentice take their place. Vader still couldn't do it alone.