If we scrap divisions and play 3 annual rivals while swapping between half o the remaining 10 teams in the league each year (for 8 league games per year), here is my list of each teams annual rivals:
UNC - UVA, dook, NCSU
UVA - UNC, VT, BC
Dook - UNC, Wake, GT
VT - UVA, Miami, Lou
FSU - Miami, Clemson, GT
Miami - FSU, VT, Cuse
GT - Clemson, FSU, Dook
Clemson - GT, FSU, NCSU
Wake - Dook, NCSU, Lou
NCSU - UNC, Wake, Clem
BC - Pitt, Cuse, UVA
Cuse, BC, Pitt, Miami
Pitt - BC, Cuse, Lou
Lou - VT, Pitt, Wake