Assuming that the guilty party's identity and responsibility have been fully determined, the traditional teaching of the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor.We live in a world surrounded by death. Abortion, murder, suicide, war, genocide, etc. Horrible atrocities abound in some parts of the world. Considering these circumstances, we must ask ourselves if killing anyone (even those guilty of the horrible crimes above) is witnessing to the value of every human life. Revenge never helps anyone, ever.
If, however, non-lethal means are sufficient to defend and protect people's safety from the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common good and more in conformity with the dignity of the human person.
Today, in fact, as a consequence of the possibilities which the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm—without definitively taking away from him the possibility of redeeming himself—the cases in which the execution of the offender is an absolute necessity "are very rare, if not practically non-existent." (CCC 2267)
From not quite as authoritative a source: