There has been continual debate over the morality of the death penalty down through history. Joseph Bottum has written a thought-provoking article on Christians and the Death Penalty. Bottum tellingly critiques various Christian arguments in favour of the death penalty. One of the most important, perhaps, is the belief that Romans 13 legitimates governments to carry out some of the punishments that Israel were originally commanded by God to do. However, Bottum argues that
the one thing no modern state can claim is that it is anointed, and the things that require anointing it lacks authority to do: the imposition of a state religion, for example, and the exaction of the death penalty, for precisely the same reason. Christians would have to engage in a national idolatry to suppose that all the acts allowed in ancient Israel are permissible in Connecticut [some of Bottum's examples come from Connecticut].
Christian proponents of the death penalty need to think about the light that the death of Jesus sheds on the issue of the death penalty. Bottum writes:
If Jesus Christ sheds light on the meaning of life and the death of every human being, we can see in that light both how blood demands repayment and how Jesus has forever done the repaying with his death... Without constant pressure from the New Testaments revelation of Christs death and resurrection, the state always threatens to rise back up as an idol. And one sign of a governments overreaching is its claim of power to balance the books of the universeto repay blood with blood.
You can find the whole article here.