A complicated subject, but I'll give my thoughts on it.
First, I don't have an unqualified and unilateral anti-death penalty stance. Rather, think that, in consonance with scripture and tradition, it ought to be reserved only, and only ever, for those cases where the person is 1) Willfully incapable of being reformed 2) Lack of any contrary evidence for guilt, the guilt having been established in a fair and just manner 3) It is carried out painlessly, humanely 4) Reserved only for the most serious crimes.
So now, let me explain why I hold to this. First, it's because as a Catholic, I believe in the sanctity of human life. All men were created in God's image, and the sinner is no less worthy than the infant in the mother's womb. Mortal sins and moral defects do not destroy the humanity of the individual person. I feel it is inconsistent to save Jimmy's life as and infant and end it when he's an adult.
The issue of 'innocence' comes up when this is mentioned, the argument being that abortion, for example, is wrong only because the infant is innocent. The murderer is guilty. This totally avoids the unpleasant fact that 'All have sinned and fallen short of the glory of God', that "None are righteous, no, not one". This is particularly a problem for protestants, for whom there is no distinction between mortal and venial sin. Stealing a penny is as evil as hacking the bank accounts of multiple poor, single mothers. The man who is being put to death is just as guilty as the man who kills him, the man who gets angry easily and lashes out at people.
The Catholic, of course, does'nt have this issue because we have the distinction between various degrees of culpability. "All sin is sin, but not all sins are unto death". This issue of 'culpability' accounts for three of my reasons, gravity of crime, established guilt, irreformability,
Because, as I noted, not all sins are equal. Some are graver than others. Even in scripture, the punishments for which death was leveled in the old testament were grave crimes. A man is put to death for having inappropriate sexual relations, not just for impure thoughts. To kill merits death, but not anger, to steal merits death but not to covet. So it ought to be, only the gravest crimes ought to merit it. Note though, when I say that the crimes merit it, I mean it only as a sense of justice, not retribution. It is not for man to execute judgment and vengeance, because the Lord said "Vengeance is mine" and "To me belong vengeance and recompense". Therefore, if the penalty is applied, it has to be done as objectively as possible. Further, even the verse that we render an eye for an eye, a tooth for a tooth, a hand for a hand, etc, is not to be taken as a command for vengeance. It is a command for just retribution, punishment must be just and can never exceed the crime. And what crimes are the gravest? Those which cause the greatest harm and in which the perpetrator is the most solidly guilty.
Guilt assumes the free act of the will and freedom from impediment to making a decision. This is why, for example, the insane are innocent of crimes. They cannot be culpable for an act they were unable to freely choose to do or not to do. An insane man who murders has certainly done something grave, but he could not choose to murder or not to murder. There was no free act, and thus no culpability. And I would say that definitions of culpability go much further than simple sanity/insanity, and that further investigation should always be in cases where grave matter exists. Rather unhelpfully for the wholesale supporters of capital punishment, scriptural standards for establishing guilt are high. Without two witnesses seeing the event as it happened, the penalty of death was not applied.
There is also the issue of reformability. God said of the souls of sinners that he wishes not their death, but that they be converted and live. Obviously, a dead man has no way of repenting, and if he really has committed a grave sin, will thus die in his sins apart from God. Following that, I think it is only just that the only ones who,wilfully and without impediment, show obstinancy in refusing to be reformed ,perhaps even a desire to continue their evil, these are those most culpable. The man who being convicted repents, ought not to die. If God would not slay the sinner who repents, why ought we? If God who commanded the destruction of cities and peoples would relent is they would repent, why ought we say that we have a better standard of justice, that even the sinner who repents still deserves death? Repentance makes innocence, to kill the repentant is to kill the innocent. Therefore, I would say that the death penalty is totally and completely unjustifiable for someone who repents and shows remorse for their action.To kill them is murder, which the Lord definitively condemns.
So those are moral arguments. You can take them as you like. But the best argument, the one that no Christian can avoid is charity. Everthing in the Christian life HAS to be evaluted by charity. The virtue of charity, of self-sacrificial love for others, regardless of earthly recompense IS the example given to us. Remember, as much as many warmongering Christians might want to deny, Christ suffered for use to leave us an example that we might follow in his footsteps. And what did Our Lord do? When reviled, he reviled not, when suffering, he threated not. He committed himself to the one that judges justly.
Every action of a Christian must be evaluted to the law of Charity, the law which says ""If it be possible, as much as is in you, have peace with all men", the law which "Rejoices not in evil, but rejoices with the truth; Bears all things". The Christian must ALWAYS remember that Justice is tempered by Charity. Strict justice required the destruction of all humankind, since were were a 'perverse and crooked race'. Under the yoke of sin, we were at enmity with God. But what did God do? "God (who is rich in mercy) for his exceeding charity wherewith he loved us Even when we were dead in sins, has made us alive together in Christ, And has raised us up together and made us sit together in the heavenly places, through Christ Jesus. That he might show in the ages to come the abundant riches of his grace, in his bounty towards us in Christ Jesus." If this is the response of God toward the greatest offense commited against him, the cold heartedness of man toward him and man's refusal to be in communion with him, event to killing his son, the innocent one, the just one.
I would wish that people would take this in mind, and truly think of it.