Here is a schedule that may be useful:
( 7 13 v 5 11) ( 9 17 v 3 6) ( 2 12 v 20 10) (19 4 v 15 14) ( 8 1 18 16)
( 8 14 v 1 12) (10 18 v 4 7) ( 3 13 v 16 6) (20 5 v 11 15) ( 9 2 19 17)
( 9 15 v 2 13) ( 6 19 v 5 8) ( 4 14 v 17 7) (16 1 v 12 11) (10 3 20 18)
(10 11 v 3 14) ( 7 20 v 1 9) ( 5 15 v 18 8) (17 2 v 13 12) ( 6 4 16 19)
( 6 12 v 4 15) ( 8 16 v 2 10) ( 1 11 v 19 9) (18 3 v 14 13) ( 7 5 17 20)
(19 16 v 6 17) (12 18 v 9 11) ( 7 1 v 3 2) ( 8 4 v 20 13) (14 15 10 5)
(20 17 v 7 18) (13 19 v 10 12) ( 8 2 v 4 3) ( 9 5 v 16 14) (15 11 6 1)
(16 18 v 8 19) (14 20 v 6 13) ( 9 3 v 5 4) (10 1 v 17 15) (11 12 7 2)
(17 19 v 9 20) (15 16 v 7 14) (10 4 v 1 5) ( 6 2 v 18 11) (12 13 8 3)
(18 20 v 10 16) (11 17 v 8 15) ( 6 5 v 2 1) ( 7 3 v 19 12) (13 14 9 4)
(11 3 v 10 17) ( 2 4 v 20 19) (12 7 v 8 9) (13 18 v 15 1) (16 5 14 6)
(12 4 v 6 18) ( 3 5 v 16 20) (13 8 v 9 10) (14 19 v 11 2) (17 1 15 7)
(13 5 v 7 19) ( 4 1 v 17 16) (14 9 v 10 6) (15 20 v 12 3) (18 2 11 8)
(14 1 v 8 20) ( 5 2 v 18 17) (15 10 v 6 7) (11 16 v 13 4) (19 3 12 9)
(15 2 v 9 16) ( 1 3 v 19 18) (11 6 v 7 8) (12 17 v 14 5) (20 4 13 10)
each player has 12 different partners, and see all possible opponents at least once and at most twice.
Hope that helps.
