That's a tougher issue. The Church has always taught that the death penalty is justifiable in principle. The latest teaching from the pope (pretty much binding) qualifies the old teaching, saying that the death penalty is still justifiable in principle BUT in countries where it is now possible to imprison criminals for life without their being a threat to the public, then the death penalty is unneccessary and should be opposed for prudential reasons.
Here is a quote from the Catechism of the Catholic Church,
CCC 2267. "The traditional teaching of the Church does not exclude, presupposing full ascertainment of the identity and responsibility of the offender, recourse to the death penalty, when this is the only practicable way to defend the lives of human beings effectively against the aggressor.I have highlighted the parts of the teaching that are the most difficult to accept.'If, instead, bloodless means are sufficient to defend against the aggressor and to protect the safety of persons, public authority should limit itself to such means, because they better correspond to the concrete conditions of the common good and are more in conformity to the dignity of the human person.
'Today, in fact, given the means at the State's disposal to effectively repress crime by rendering inoffensive the one who has committed it, without depriving him definitively of the possibility of redeeming himself, cases of absolute necessity for suppression of the offender 'today ... are very rare, if not practically non-existent.' [Cf. Gen 4:10 .]"