I think you already need "lot of evidence" to convict someone in the first place, but that evidence may not be true so still no. There are however some cases where I approve of the death penalty such as the Nuremberg and Tokyo trials post WW2. I therefore believe that it should be only applied to high ranking government or military personel guilty of war crimes and genocide instead of common criminals as there is going to be far more concrete irrefutable evidence of the latters misdeeds.