Little help here!
What part of the Constitution covers this?
The 8th Amendment ban against Cruel and Unusual punishment.
This amendment is open to intepretation. It is a bit like a 2nd Amendment for the anti-capital punishment crowd.
I think their opinion on it is worth respecting. It is good to show respect for an alternative interpretation even if you disagree with it.
This is a limitation on the state’s power just as the 2nd limits the state from infringement on the right to carry arms.
Exactly where the limit is, is subject to debate and has changed over time.
The Wikipedia article is remarkably balanced on the issue:
http://en.wikipedia.org/wiki/Cruel_and_unusual_punishment