The level of evidence required to find someone guilty of murder should be the same whether or not the death penalty is on the table. But I don’t think that it should ever be on the table.
I’ve sometimes been tempted to say that anyone who wants to have someone put to death should be so certain of the convict’s guilt that they would be willing to bet the lives of their own children on that fact. (After all, they’re willing to be the lives of other people’s children.) But it’s a moot point because the death penalty would still be wrong even if we could all be 1000% certain that no innocent person would ever be executed.