From my reading in the bible, they're also unbiblical on this issue. God specifically indicated that the proper punishment for murder was death.
"Execution Of Criminals
Another kind of lawful slaying belongs to the civil authorities, to whom is entrusted power of life and death, by the legal and judicious exercise of which they punish the guilty and protect the innocent. The just use of this power, far from involving the crime of murder, is an act of paramount obedience to this Commandment which prohibits murder. The end of the Commandment is the preservation and security of human life. Now the punishments inflicted by the civil authority, which is the legitimate avenger of crime, naturally tend to this end, since they give security to life by repressing outrage and violence. Hence these words of David: In the morning I put to death all the wicked of the land, that I might cut off all the workers of iniquity from the city of the Lord."
The Catechism of Trent (The Roman Catechism) 1546
The opposition to the death penalty is actually a novel opinion which departs from infallible Church teaching on the issue. To support the legitimate use of the death penalty is quite Catholic, and quite faithful to Magisterial teaching.