Could you elaborate a bit more on what you are doing and what you want to achieve.
In special on where are you publishing your reports (I assume Tableau server?).
As you mentioned that you have a parameter, you could embed a unique workbook in your sites and in each site pass the parameter of the Country that is related to that site. If your parameter name is "Country" you can add ?Country= and the country code to pass the parameter in the embed URL.
Mora about this here:
I hope this helps