Hello Greg,
Well, I meant root directory of the project which is placed on server. Nevertheless, there are basically two ways of changing favicon - the first is to replace the default icon and the second one is programatically but I suppose none of them are possible for you since you do not have access to the project directory or code files. You will have to contact your administrator to give you access or he can change the icon himself.
There is also a
FavIcon web part available on Kentico Marketplace which is designed exactly for this purpose but it is not for free so I am not sure if it is the best option for you.
Best regards,
Filip Ligac