It's probably a modern fake, but I doubt if you'll know without putting it in a experts hands, unless someone knows a "tell" on the fakes. I will throw out one thing. The color may seem odd for a silver coin, but I have owned a handful of the 500, 1000, and 2000 Reis coins from that series and the coloration seems to be typical. While a nice coin, the 2000 Reis is not a very high priced coin and it would seem likely that the coin may be authentic, but the countermark may very well have been added.