First, you have to know what a coin is. The numismatic definition, as stated in Webster’s is, “A small piece of metal, usually flat and circular, authorized by a government for use as money.” Another attribute not in Webster’s but usually associated with coins is that they have a standardized value. (and weight when most coins were of precious metal and worth that weight in metal as minted) That distinguishes a coin from medals and other bits of metal or other materials valued strictly by weight or other intrinsic characteristics.
The first coins imprinted with identifying marks by a government to be used as a standard medium of exchange were from Lydia in the 8th Century BC. All other “money” or medium of exchange before that was privately made and the design on it, if any, carried no significance.
That said, there was nothing issued by governments and therefore images glorifying the head of state or other officials would have been completely meaningless and pointless.
That doesn't mean they weren't coins.
Besides, today's coins are put together out of materials of no significant intrinisc value.
A good match for what we mean by coins today probably first occurred in the Shang dynasty. Those are the guys who developed the first known writing system in China proper.
Try: http://chinesecoins.lyq.dk/History/Coin_history_Shang_to_Warring_States.htm