What is probably the oldest form of execution, being used as far back as Biblical times?
This is for a criminal justice course, in relation to the death penalty. So citing early documented murders is not what is being looked for, but rather more official means of ending life.
In your question, you mention that this form of execution dates back to Biblical times. This can give us a good hint as to what form of execution is being referred to. The form of execution that is most closely connected to the Bible is stoning. Stoning is often mentioned (as in the New York Times link below) as one of the most ancient forms of execution.
For example, in Chapter 20 of the book of Leviticus in the Bible, there is given a list of crimes for which people should be put to death. The only form of execution mentioned in that chapter is stoning.
So, the form of execution that goes back to Biblical times is stoning.
stoning and hanging and crucifing them as jesus was done might be some