Is there any scientific evidence that non-harmful spanking does or does not exist? Furthermore, is it ever effective (whether or not it is harmful)?
Here is the resolution on corporal punishment by the American Psychological Association.
The resolution includes this part:
This indicates that punishment can be used effectively. However, there are a number of variables that make it generally impractical, as mishandling these variables will most likely result in severe negative consequences, in addition to failing to adjust the behavior as intended.
Unfortunately I do not have direct access to the research that the association referenced to arrive at this resolution.
Here is the problem with most studies conducted on children. Todays mainstream view on spanking is if you spank a child you'll produce an aggressive individual.
Here is a youtube link, it would be good to look at the whole video (24minutes) because you'll lack context if you watch only the part about parenting that starts at 18:28:
What I wanted to offer from the start to person who asked the question is caution when s/he looks at studies and answers, because in psychology/pedagogy while there are a lot of brilliant scientists, lot of scientists from these fields don't understand the basic scientific principle and don't have scientific integrity. S/he needs to be very skeptical when s/he follows the advice given here or from the associations of psychologists.
It is easy to do a biblical study. Here is a great resource: http://parentingfreedom.com/discipline/
And non-harmful is hard to evaluate. For example Lydia Schatz was beaten to death and the cause of death was rhabdomyolsis. This is a break down in the muscle fibers that lead to kidney or heart failure. So a parent might not see what is happening internally (physically). And of course internally emotionally