There is only one solution to the death penalty on which we can all agree: ABOLISH IT.
I believe this result is commanded not by morality, but practicality. Look, let's group everyone into two categories: Those who believe the death penalty is never justified and those who believe it is sometimes appropriate. The first group, of course, wants to abolish the death penalty.
Turning to the second group, taken any average person who believes the death penalty is an appropriate penalty for certain crimes -- like myself -- and tell that person that each time a person is executed, the taxpayers pay more than DOUBLE what they would have paid if the person were simply jailed for life (because of all the appeals they get, the legal fees, the special in-prison procedures, etc.). Now I see no problem with the death penalty from a moral standpoint, but I don't know anyone who is SO adamant that a prisoner MUST die rather than spend life in prison without chance of parole, that they want to spent a lot more money to make that happen.
I am certain if you take all the people who morally oppose the death penalty, and add in all those who agree as a practical matter that if it will cost a lot more to impose the death penalty than a life sentence (without parole), they could live without the death penalty, and I think that includes pretty much every sane person in America.
I imagine those who are left are people who have had a loved one die at the hands of a criminal and feel a desperate longing to have that criminal lose their life. I sympathize with that. However, I do believe there is some consolation that life in prison without chance of parole is not exactly a slap on the wrist. One could even argue the better justice is to give the person as much time as possible to reflect on their wrongdoing, thus increasing the likelihood they will reach a turning point where they recognize the error of their ways and feel true remorse for what they have done.
There is even some gravy to this position -- I use gravy to refer to any added extra benefit. One rarely discussed argument against the death penalty is that it requires we, as a society, to have a legal job of executioner. What must having that job do to a person's psyche? What about those who indirectly participate in the execution? The governors who fail to grant a stay of execution? The guards who walk the person to the death chamber? I think participating in such a thing may be a heavy burden for them, and I think there is something noble -- if not morally required -- in a society saying, "No, we will not legalize the killing of any human being in cold blood." (Note that the "cold blood" qualification means we can still kill in the hot blood of self defense and defense of others, whether we are talking about a police shoot out, a battlefield, or a private citizen defending his family.)
Lastly, I expect there will be those who say that my common sense solution assumes that death penalty cases cost more than imprisoning a man for the rest of his life. I expect there will be those who say that, even if that is true, a better solution would be simply reducing the cost of death penalty cases. Get rid of all those appeals and special procedures. Hell, take them out back and hang them as soon as the verdict is read! To those people, I say that, right or wrong, that is simply NOT how our criminal justice system works, nor is there a snowball's chance in hell that will ever become how our criminal justice system works barring a cataclysmic descent of our society into total anarchy. I would point out another possible "solution" is to raise everyone nice so no one hurts anyone else-- again, not gonna happen. Impractical and impossible solutions are no solution at all.