Sister Helen Prejean: The cross and innocence
(Particular focus on innocence @5.30 mns)

"Capital punishment is a method to irremediable mistakes"
Reformed Church in America

Here are opinions selected from the internet explaining generally why some religious people are concerned by the issue of innocence and finding alternative methos to help tackle crime

We therefore have to seek methods of dealing with violent crime which are more consistent with the Gospel's vision of respect for life, and Christ's message of God's healing love. In the sight of God, correction of the offender has taken preference over punishment, for the Lord came to save and not to condemn.

U.S. Catholic Conference, Committee on Social Development and World Peace, 1312 Massachusetts Avenue, N.W., Washington, DC 20005

In view of our responsibility as ministers of reconciliation we confess that we have not adequately fulfilled our obligation to work for the abolition of capital punishment or for the reduction of crime in our society. We need to be more faithful in serving persons in prison and in laboring for the reform of prison procedures; for the rehabilitation of released prisoners; and for the improvement of the economic, social, and religious conditions which contribute to the making of juvenile offenders and to the spread of crime. (...) -  And we pray that God may grant us wisdom, vision, and courage that as a brotherhood we may engage in this ministry as the Holy Spirit gives us direction.

General Conference Mennonite Church

This church recognizes the need to protect society from people who endanger that society: removing offenders from the general population, placing them in a secure facility, and denying them the possibility of committing further crime (i.e., incapacitating them). Our challenge is to incapacitate offenders in a manner that limits violence, and holds open the possibility of conversion and restoration.

Evangelical Lutheran Church in America