Do you assign partners or do the pairs stay together the whole time? If the latter you will need to have eleven rounds and each pair will have a bye at some point.
If eleven rounds isn't possible, you could have a swiss guided round robin. After the first round choose a round which has as many leaders playing against each other as possible.
In the following, pairings against 12 show a bye for that round.
11 or 12 players
Rd Pairings
1: 1-12 7-6 11-2 8-5 10-3 9-4
2: 12-7 2-1 6-8 3-11 5-9 4-10
3: 2-12 8-7 1-3 9-6 11-4 10-5
4: 12-8 3-2 7-9 4-1 6-10 5-11
5: 3-12 9-8 2-4 10-7 1-5 11-6
6: 12-9 4-3 8-10 5-2 7-11 6-1
7: 4-12 10-9 3-5 11-8 2-6 1-7
8: 12-10 5-4 9-11 6-3 8-1 7-2
9: 5-12 11-10 4-6 1-9 3-7 2-8
10: 12-11 6-5 10-1 7-4 9-2 8-3
11: 6-12 1-11 5-7 2-10 4-8 3-9
