Firstly, the meaning of 'persuasion' needs to be defined:
The noun form of 'persuade'.
1. to prevail on (a person, etc.), by advice, urging, reasons, inducements,etc., to do something.
2. to induce to believe, convince.
(points 1. and 2. are the Macquarie Dictionary (2004) definitions of 'persuade').
'Persuasion' is an activity limited to communication between sentient (conscious/aware) beings, such as person to person, shepherd to sheep,
and dog-owner to dog. I believe the context of the question is most likely interested only in human social affairs, so I'll confine the answer to such.
Through, by far, most of human history, and pre-history, non-violent methods of resolving conflicts have been far more common than violence. Violence, for this argument, are acts such as threats, stand-overs, ridicule, false rumour-mongering as well as the obvious: physical violence.
Persuasion tends to be usually non-violent, so can be classed as a humanly-progressive behaviour choice.
As violence usually only results in changing behaviours but not minds, I feel it can be assumed as most likely that through the enlightenment of spiritual and religious studies, and in more recent centuries from within philosophical, theosophical and psychology schools of thought, people developed skills in persuasion because violence is too costly in human terms, as well as inadaquate and innefficient for social interaction and adaption.
Considering the above notions, it seems to me that persuasion would predate higher language and record-keeping, let alone story-telling, so we cannot be sure, in a factual sense, of how, where or when persuasion developed. Belief is another matter...