Read Edward Feser: "By Man Shall His Blood Be Shed: A Catholic Defense of Capital Punishment."  He puts forth a very compelling case.  Since he argues for the position far more ably than I can---give it a read. 

I want to note that he has written many other works on philosophy which from my view are very good.  They challenge contemporary metaphysics--which is based largely on Hume and the modern philosophers. Feser is no easy read, however.  If you do dare to read him, you better make sure you have some time on your hands and are wiling to struggle with very heady concepts.