The reason it works for the ACC is because it allows all the other remaining teams to be split into two and played every other year.
You're looking for
A + 2B = X-1
and
A + B = Y
where
A is the number of 'permanent rivals'
B is the number of other teams played in a year
X is the conference size
Y is the # of conference games
For a 12 team league, that means (in an 8 game conference slate) setting 5 permanent rivals and rotating the other 6 (3 per year)...which is basically divisions