As you probably know, the footballer's name is
Arthur Antunes Coimbra. According to this site:
http://www.ofutebol.com/nicknames.shtml his sister called him Arthurzico, an alternate diminutive of Arthurzinho meaning "little
Arthur," which was shortened to Zico. I have not been able to find evidence that others use -zico as a diminutive, so it might have just been a family-specific nickname that was intended to mean "little," without any actual meaning in Portuguese.
~~~~~~~~~~~Amanda~~~~~~~~~~~