Libertarian Death Penalty

A Libertarian Argument for the Death Penalty
My Libertarian response:

In order for rights to mean anything, they must be inalienable.

The difference between the murderer and the thief is that the murderer does not represent a threat because you have already denied him his liberty. The thief on the street is a threat to the rights of others, and this may justify violating his right to liberty.

I don't think killing murders is justice at all. I think justice needs to be based on restitution. The thief should be forced to work to pay for the what was stolen and any incidental damages. The murderer should live a long and productive life, the proceeds should go to pay for his trial and imprisonment, and to the families of the victims. Justice is about setting things right, as much as is possible.

If rights are alienable, then you have the question: What alienates them? does a man give up is right to life by shooting his wife's lover? What about attempted murder? mere assault? rape? If a stranger abducts, tortures and rapes your daughter, can you kill him then? I know what the instinct is, but does that really alienate his right to life? Where do you draw the line?
Once you give the state the power to draw that line, it can draw it wherever it wants.
Do you give up your right to life by committing the treasonous act of exposing the crimes of the President?

And the the question of certainty remains. You acknowledge this, but you also say "Assume for purposes of argument that there is no doubt of his guilt. He’s admitted the crime and is proud of it." I would say that this is not enough, and that having no doubt, or even no reasonable doubt, is inherently impossible.
Demonstrating any doubt is easy: He might be controlled by martians, so none of it is his fault. It could happen to anybody.
So to convict anybody at all, we have to allow only reasonable doubts. The thing is, every conviction is supposed to be beyond a reasonable doubt. Reserving the death penalty for cases that are 'really beyond any reasonable doubt' only highlights the fact that juries are incapable of considering reasonable doubts, or willing to convict anyway. We know we have false convictions at every level from parking tickets to murder. I would posit that in the vast majority of cases, if something actually happened (like innocence) then it was a reasonable possibility that the jury ignored.
If we completely revamp our legal system, and then go 100 years with no false convictions for anything, then this could be reconsidered.

To recap:
We shouldn't kill defenseless people.
We are too vengeful to let our instincts define justice.
We are too stupid to figure out what happened, so we shouldn't kill people no matter what we think they've done, or how sure we think we are.