Dr. Benjamin Rush was one of the earliest notable American opponents of the Death Penalty. As will be seen, his anti-capital punishment position was derived from his understanding of the Bible. Regarding his theology, Rush described it as "a compound of the orthodoxy and heterodoxy of most of our Christian churches." Basically, formerly a Calvinist, he converted to Arminianism, remained orthodox on matters of original sin, the trinity, incarnation, and atonement, but believed in universal salvation through Christ's universal atonement. In short, he was a liberal Trinitarian Christian Universalist.
You can read the primary source on googlebooks, indeed a book so old that the "s's" still look like "f's." He notes the case of the woman about to be stoned to death for adultery -- a capital crime in Old Testament times -- where Jesus forbade her execution. Though Rush doesn't explicate it, the literal meaning of Jesus' words "Let he who is WITHOUT sin," suggests that only God (or if Jesus were not God, a uniquely sinless human like him) is qualified to implement capital punishment. WITHOUT Sin. Not "you may have problems of your own, you hypocrite," but WITHOUT Sin.
Here is a short passage from Rush's writings. By all means, read the entire context.
[W]hile I am able to place a finger, upon this text of scripture, I will not believe an angel from heaven, should he declare that the punishment of death, for any crime, was inculcated, or permitted by the spirit of the gospel.
It's the same theologically liberal hermeneutic of, instead of appealing to specific "proof texts," abstracting general principles from the "spirit" of scripture to reach specific conclusions not mentioned therein, that also made the Christian case against slavery. The Bible nowhere specifically abolishes slavery; to the contrary many specific texts recognize its validity. It's only by taking the principle that because all men are created in God's image, they are equal, and then applying that to slavery, that the "spirit" of the Bible likewise can be said to be anti-slavery as it is anti-death penalty.
The death penalty and slavery are good examples of social issues where the Bible gives no clear cut answer and texts can be offered on both sides. (On slavery, I'm inclined to argue the Bible is a pro-slavery book, or at least one utterly unconcerned with its abolition.) History, not hermeneutics, answers the question. History has answered the question with slavery; it's still out on the death penalty.