Would it be illegal to carry my Co2 .177 caliber pistol witch a license is NOT needed for on me for self defense purposes in public or on private property like in my house or in my yard?

You might wish to consult with those a bit closer to you as to how the laws apply in your jurisdiction.

http://en.wikipedia.org/wiki/Gun_politics_in_South_Africa

That link includes contacts in your country.

Many things that are tec legal could be a issue,
1. are you a citizen of that county ?

But what I would worry about is, police not knowing it was a CO2 and finding out after you are either shot or on the ground bleeding.
Or they arrest you for disturbing the peace,

Why do you want to carry it on your person like that.