I did some searching, and it turns out this question was raised on this very message board many moons ago! @Fr_of_Jazz (unsure if he still posts here or not) wrote an outstanding summary of this topic, which I will copy/paste here and in a second post because 3200 character limits are silly sometimes.
(1) A summary of what Catholics need to believe in faith and morals, i.e., the content of the Catholic Faith, can be gained from The Catechism of the Catholic Church, other summary documents such as theCompendium of the Social Doctrine of the Church, and other teaching documents like JPII Evangelium vitae. The issue of capital punishment is addressed in all of these.
(2) If one wants to dig deeper than even the Ecumenical Councils and explore ad hoc acts of the Church’s magisterium at various points in history, they need to employ some hermeneutic tools. As I’ve said in other contexts, if one wants to ask adult questions then they have to be willing to go beyond 4th grade answers.
_(3) Tools: _
One needs to consider among other things–
(a) the historical and cultural context of the statement;
(b) what event(s) or proposition(s) occasioned the statement;
© the exact wording of the statement;
(d) the subject matter, i.e., is it dogma, morals, or contingent social/political situation calling for a contingent judgment
(e) what level of authority is being exercised as made clear in the wording.
(f) subsequent doctrinal and moral developments often providing broader contexts; and contingent judgments responding to changing social, cultural, and political contexts.