By using PROC OPTMODEL in SAS/OR, you can find both an 8-year schedule with no repeats (version 1) and a 6-year schedule with no repeats and with each couple giving to each of the comb(4,2) = 6 other pairs exactly once (version 2). The code is attached.

The couples are {1,2}, {3,4}, and {5,6}.
For version 1, PROC OPTMODEL yields:

3 4 5 6 2 1
5 3 6 1 4 2
4 6 2 5 1 3
3 5 6 1 2 4
4 6 1 5 3 2
6 3 5 2 1 4
5 4 2 6 3 1
6 5 1 2 4 3

For version 2, PROC OPTMODEL yields:

4 3 5 6 2 1
5 4 6 2 1 3
3 5 1 6 2 4
4 6 5 1 3 2
6 5 1 2 4 3
3 6 2 5 1 4