I just crossed the border from Serbia to the Republic of Macedonia and was surprised that the currency exchange booth on the Macedonian side accepted Euros but not Serbian dinar.
Generally I've found even in places that are not very friendly at least at the border it's possible to exchange money if not elsewhere.
Does this mean that I won't be able to change my Serbian money for Macedonian money? I didn't expect Macedonia to be on unfriendly terms with Serbia.
According to the girl at the reception here at a hostel in Skopje there is an Exchange office in the Ramstore mall, next to the museum of Skopje. There they do exchange RSD, however I have not tried this myself. Worth a try.
(I'm promoting and editing my comment to an answer since we haven't received anything better)
While I was there (almost a week) I found only one exchange place in Skopje which didn't list RSD but did buy them when we asked about it (no selling though). The rate was terrible, about 25% below the official rate!
I was suggested to try the bus station but never tried as I managed to swap some cash with a traveller in my hostel heading the opposite way.