An FAA private pilot certificate includes night flying privileges. An instrument rating is not required to fly at night.
An FAA certificate extends privileges to the holder when operating within the FAA's jurisdiction. When operating in a foreign country, one is subject not only to the regulations pertaining to one's own certification (FAA, in this case), but also to those of the foreign country.
Interestingly, an FAA commercial certificate requires an instrument rating, or the holder is restricted to flights for hire to daylight, and within 50 nm. I had one of those myself for the first five years of my commercial career. I didn't hold an instrument rating (I was an ag pilot, and didn't need one). My certificate stated "Flights for hire at night and at distances greater than 50 nautical miles, prohibited."
I could fly at night all I wanted without the instrument rating...just not for hire. Were I to have taken that certificate to another country, however, the rules and regulations prescribed by the FAA would still have governed me. Additionally, the rules of the country in which I would be operating, would also govern me. If that country prohibited flight at night without an instrument rating, then I wouldn't be authorized to fly at night, period. The fact that in the US I could do so would be irrelevant.