Just to confuse the issue
Up until Cyprus joined the EU, Cypriots born on the British Base areas can get British passports, but not automatic right of abode. (I'm not sure what happens now)
I have nephews in the UK whose Grandfather was a Cypriot, but took British citizenship during the 30+ years he lived in the UK, their Father was born in the UK and never lived anywhere else and their Mother is English, they are British Passport holders and they have never resided in Cyprus, in fact they've probably only ever spent about 8 weeks of their teenage lives here, can't speak a word of Greek and know as much about Greek/Cypriot culture as I do about the surface of Pluto, but if they stayed here for 6 months or more they have to do military service as they are deemed to be Greek Cypriot.
I have a Cypriot passport after living here for 14 years, but my son is not allowed to join the Cypriot army....(not that he wants to!)
None of my children has taken Cypriot citizenship.
I have met 3 generations of an Egyptian family that all have British passports, although none of them has ever been to the UK, the right to these passports goes back to the "Colonial Days"
Hincyprus, I believe your Grandson can take both British and Montenegron citizenship.