That's where your argument fucks up. Anybody convicted by a court is supposed to be definitely guilty not just probably guilty but the truth is you can never be 100% sure that someone is guilty and that's why the death penalty should be banned. How many people are found to be not guilty after new evidence emerges years later? If you've killed the poor sap then unless you go all Frankenstein on his ass you ain't never bringing him back to life to accept his apologies and huge compensation cheque. There's no such thing as a perfect justice system but one where life imprisonment in reasonable conditions means just that with no parole or early release is as close as a fallible world will get to fairness. If you murder someone with the backing of the state then, i'm sorry, but that's just what it is, murder and probably worse than some murders because it is planned and sanctioned. Every human being deserves the right to fair treatment whilst incarcerated for whatever crime by the state. What any victim's family decides to do about it is of course another matter 
I don't see that proof beyond ALL doubt, not just reasonable doubt, fucks my argument up. Like I said..DNA evidence is a powerful thing, as is a signed and sealed confession of a person deemed mentally competent, that is videoed to verify that the person was not forced to confess due to someone holding a gun to his head, making threats or some shit like that. If some guy confesses to raping a child, and his sperm DNA is found in said child's orifice, well....that is proof beyond ALL doubt, and it is rock-solid proof of the crime. In that case, I would be 100000% sure the molestor is guilty, and wouldn't hesitate one millisecond to put his sorry ass in Ol' Sparky.
In many cases, the people who were found guilty and subsequently found innocent, it is because of DNA, and years ago, it was substandard, or just unavailable. These days, that is hardly the case.
I don't consider implementing the death penalty as murder. It is called justice. A life in prison is hardly punishment anymore. They live better than alot of free people. They get their three meals a day, live in air conditioned comfort, watching cable TV and getting college educations. Meanwhile, we have children who are lucky to get one meal a day because their parents are out of work, homeless people who fell on hard times but STILL manage to suffer a day-to-day existence without committing a single crime. And these unfortunate, LAW ABIDING people could only WISH to have it as good as our convicted murderers. At least they get hot meals and a roof over their heads when it rains. And TV. and a hot shower. and access to the legal system, to file frivolous lawsuits about "they won't give me chunky peanut butter! my civil rights are being abused! I'M GONNA SUE !!!" Meanwhile, the homeless family can't even qualify for food stamps.
And I do not agree that
every human being deserves the right to fair treatment while in custody. Their victims deserved rights, but that wasn't on the criminal's mind at the time of the crime. If a person doesn't give a shit about the rights of the victim, then fuck their rights when they get found guilty.
And re: execution being worse than some murders because it is planned and sanctioned..are you NUTS?? How is a peaceful death by going to sleep with lethal injection, just going night-night and not waking up, with no physical suffering, as bad as someone beating another to death with a hammer? That is just insane to even suggest that execution for a crime is anywhere near as bad or even in the ballpark of 'the same' as a murder.
And the part about 'what any victim's family decides to do about it....' ...well, that's just wishful thinking, because we would just arrest the family and a whole 'nother court case would get started up (yet another glitch in our legal system). I would love nothing more than to have proven criminals tied to a chair in a soundproof room, and then let the victims and/or their families have a go at them. We could let them bring a weapon of choice, preferably the same weapon used on the original victim.
All too often, the state makes plea deals with criminals, much to the horror and disbelief of the victim/family. There are way too many people concerned with treating the criminal justly, and not near enough people concerned with doing the VICTIM/FAMILY some justice.