It can work for 7 months, where all pairs of teams play exactly once:
Mnth Hse Tbl1 Tbl2
1 1 2 6 3 5
1 2 1 8 4 7
2 1 1 3 5 8
2 2 2 7 4 6
3 1 4 8 5 6
3 2 1 7 2 3
4 1 1 2 4 5
4 2 3 7 6 8
5 1 1 6 2 8
5 2 3 4 5 7
6 1 2 4 3 8
6 2 1 5 6 7
7 1 1 4 3 6
7 2 2 5 7 8
You are then free to choose anything for month 8, but you could have a play off with the best two teams paired, then the next best, and so on.
Hope that helps,
Ian