The Vatican's position is that it opposes capital punishment. It's the normative Roman Catholic teaching, although as far as I know one can still be a Catholic in good standing if he or she still favors capital punishment.
Me, I think the arguments are stronger in favor of capital punishment, not about justice so much, but especially Dennis Prager's argument that murderers tend to kill again in prison, guards or fellow prisoners. Once you can bring yourself to kill a fellow human being, adding another to you list isn't a big deal.
So, Prager argues, if and when the murderer murders again, the moral responsibility lies with those who kept him from his deserved justice and fate.
I've tended to agree with that unassailable logic.
My best and perhaps only counterargument has been that executing a human being dehumanizes his executioners.
His name is Romell Broom. I could call him a convicted rapist and murderer---which he is---but I think we should call human beings by their names.
In Ohio a few days ago, the state sent Romell Broom to go meet his Maker. Mercifully, by lethal injection. In theory, you just go to sleep. Eternal sleep.
You can read about what happened here.
In short, they tried to find a usable vein to deliver the lethal injection but couldn't find one. They tried for hours. Hours. In fact, Romell Broom tried to help them find one. He pinched his arm, he rolled over onto his stomach.
Finally, the warden called the governor and told him of the difficulties. The governor postponed Romell Broom's rendezvous with destiny for a week, the execution is scheduled for then.
"What Would Jesus Do" is an often-abused political question. But He wouldn't do this or be any part of it, and more importantly, He wouldn't ask his followers to do this, far lesser mortals than He.
He wouldn't put them through it, no way, no how. Vengeance is Mine, saith the Lord, and that means vengeance belongs to God, not man. "Vengeance" doesn't mean revenge, it means justice.
No to capital punishment. I guess I just made up my mind, finally. Wish I knew why it took me so long...