There is no situation whereby execution is acceptable.
My opinion. Yours may differ. This is OK, we can still be friends.
Here's my reasoning:
Murder is wrong. Murder is always wrong. Killing in some situations (self-defence, etc) can be justified, but murder is always wrong. Murder is taking a life having planned to do so. The longer the time between the plan and the act, the worse it is.
Execution is murder.
Not only that, it is murder by civil servant.
Paying somebody to murder.
A contract killing.
No society can stand up and call itself just, if it stoops to that. There are no exceptions.
I am aware that some of you believe it is a better option because it's cheaper. I could explain why it isn't, actually, but I'm not going to bother, because I don't think we can justify murder for economy.