First, it's important to realize that there is danger in inserting "Capote's opinion on the death penalty" just because this is a novel. In pretty much ANY other case, I would suggest that you steer clear of stating an author's opinion, focusing instead on the provable opinions of the characters. HOWEVER, because Capote himself called this a "nonfiction novel" and was known in interview after interview to state his opinions on the subject I find it fairly safe to admit the answer to your question: Capote was most certainly against the death penalty. Further, the title serves to suggest that the murderers were people who are victims of a self-righteous society.
Capote strives to show us that murder is murder. The death penalty is murder by the state. The Clutters' deaths account for murder by two people: Dick and Perry. There is no difference. I really like the way eNotes educators have put this in the past:
But Capote's questioning of the relevance and righteousness of small-town values and priorities could be his own angry criticism of the world he himself inhabited: a false meritocracy in which his talents were inadequate unless accompanied by a biting, unrelenting charm.
Therefore murder done by a person isn't okay, but murder by the government is perfectly fine. Such is the small-town self-righteousness that Capote is criticizing. Capote believes that this error is the only thing that allows a small town to create the semblance of order after a tragedy such as this. Capote's "nonfiction novel" says it this way:
There is considerable hypocrisy in conventionalism. Any thinking person is aware of this paradox; but in dealing with conventional people it is advantageous to treat them as though they were not hypocrites. It isn't a question of faithfulness to your own concepts; it is a matter of compromise so that you can remain an individual without the constant threat of conventional pressures.
We can go even further if we consider the age old debate of nature vs. nurture. This is where Capote attempts (succeeds?) in convincing his reader about this topic. Capote is most DEFINITELY on the side of nurture! This means that Capote believes that humans are fully a product of their environment. Childhood tragedy and abuse is the reason behind the murders. We can see quite a bit of Capote in Perry who ditches conformity, is the victim of a society convinced it is always right, and shares many aspects of personality, including considering himself to be the opposite of the "manly" Dick. The confirmation of the nurture theory comes when Perry not only admits to killing the Clutter family, but also admits the following:
Maybe it's just that the Clutters were the ones who had to pay for it.
The big question is, what is "it"? The answer is this: a lifetime of abuse, mistreatment, and neglect. The reader understands and begins to sympathize with the "cold-blooded" killer. Knowing this (and believing this) is supposed to make the reader be completely against the death penalty. Again, eNotes nails the true reasoning according to Capote:
The true tragedy, according to Capote, is not the Clutter murders, which are an accident of fate, but the murder of Smith by a society that failed him as a child and shunned him as an adult.
However, keep in mind that it is the character of Brooks that can serve as Capote's true voice here. Brooks continually questions capital punishment making the title the ultimate irony.
Thus, even though the rhetoric is subtle, it is obvious that Capote sympathizes with both Perry and Dick. Further, Capote wants US (his readers) to sympathize with them as well.