Opposing execution isn't a "doctrine" of the Catholic Church. John Paul II (who isn't even pope anymore) said he personally didn't like the death penalty, but he acknowledged that he couldn't change church doctrine.
2265 Legitimate defense can be not only a right but a grave duty for one who is responsible for the lives of others. The defense of the common good requires that an unjust aggressor be rendered unable to cause harm. For this reason, those who legitimately hold authority also have the right to use arms to repel aggressors against the civil community entrusted to their responsibility.2266 "The efforts of the state to curb the spread of behavior harmful to people's rights and to the basic rules of civil society correspond to the requirement of safeguarding the common good. Legitimate public authority has the right and the duty to inflict punishment proportionate to the gravity of the offense. Punishment has the primary aim of redressing the disorder introduced by the offense. When it is willingly accepted by the guilty party, it assumes the value of expiation. Punishment then, in addition to defending public order and protecting people's safety, has a medicinal purpose: as far as possible, it must contribute to the correction of the guilty party.
2267 "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.
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 rare, if not practically non-existent.' "
So, there you have it.
PS. And might I add that my own view on execution is 100% consistent with that of the Catholic Church.