As a practicing Catholic, I will not support the death penalty as this goes against the Church's teaching, which essentially states that "the case in which an inmate should be executed is very rare if not completely nonexistent." So, if the prisoner is guilty of an especially heinous crime, then yes, the death penalty might be acceptable. But, we also have to take in the family of the inmate. Did they do anything wrong? What about his little daughter who is ten years old. What did she do to deserve this? Or the inmate's brother or sister? Why is the family being punished while the family of the victim just gets to see the inmate suffer, along with his family who did nothing wrong? While I can sympathize with the victim's family to some extent, we should never wish another human to suffer death so that we can feel some fulfillment. Also, if the person is innocent, that just contributes to the suffering on our planet.
I would, however, recommend a more strict prison system. If an inmate is justly convicted of murder, then they should be given solitary confinement for many years, with very limited social interaction.