I am not sure exactly what you mean by the placement, North, South, East and West. So would the following schedule, where each player has 36 different opponents work?
Hope that helps,
Ian.
(19 42 47 31) (1 43 40 35) (48 29 16 38) (24 2 11 39) (8 14 13 23) (41 26 12 5) (6 37 4 20) (25 36 32 22) (21 17 28 10) (15 33 45 46) (3 7 30 27) (34 18 44 9)
(20 43 48 32) (2 44 41 36) (37 30 17 39) (13 3 12 40) (9 15 14 24) (42 27 1 6) (7 38 5 21) (26 25 33 23) (22 18 29 11) (16 34 46 47) (4 8 31 28) (35 19 45 10)
(21 44 37 33) (3 45 42 25) (38 31 18 40) (14 4 1 41) (10 16 15 13) (43 28 2 7) (8 39 6 22) (27 26 34 24) (23 19 30 12) (17 35 47 48) (5 9 32 29) (36 20 46 11)
(22 45 38 34) (4 46 43 26) (39 32 19 41) (15 5 2 42) (11 17 16 14) (44 29 3 8) (9 40 7 23) (28 27 35 13) (24 20 31 1) (18 36 48 37) (6 10 33 30) (25 21 47 12)
(23 46 39 35) (5 47 44 27) (40 33 20 42) (16 6 3 43) (12 18 17 15) (45 30 4 9) (10 41 8 24) (29 28 36 14) (13 21 32 2) (19 25 37 38) (7 11 34 31) (26 22 48 1)
(24 47 40 36) (6 48 45 28) (41 34 21 43) (17 7 4 44) (1 19 18 16) (46 31 5 10) (11 42 9 13) (30 29 25 15) (14 22 33 3) (20 26 38 39) (8 12 35 32) (27 23 37 2)
(13 48 41 25) (7 37 46 29) (42 35 22 44) (18 8 5 45) (2 20 19 17) (47 32 6 11) (12 43 10 14) (31 30 26 16) (15 23 34 4) (21 27 39 40) (9 1 36 33) (28 24 38 3)
(14 37 42 26) (8 38 47 30) (43 36 23 45) (19 9 6 46) (3 21 20 18) (48 33 7 12) (1 44 11 15) (32 31 27 17) (16 24 35 5) (22 28 40 41) (10 2 25 34) (29 13 39 4)
(15 38 43 27) (9 39 48 31) (44 25 24 46) (20 10 7 47) (4 22 21 19) (37 34 8 1) (2 45 12 16) (33 32 28 18) (17 13 36 6) (23 29 41 42) (11 3 26 35) (30 14 40 5)
(16 39 44 28) (10 40 37 32) (45 26 13 47) (21 11 8 48) (5 23 22 20) (38 35 9 2) (3 46 1 17) (34 33 29 19) (18 14 25 7) (24 30 42 43) (12 4 27 36) (31 15 41 6)
(17 40 45 29) (11 41 38 33) (46 27 14 48) (22 12 9 37) (6 24 23 21) (39 36 10 3) (4 47 2 18) (35 34 30 20) (19 15 26 8) (13 31 43 44) (1 5 28 25) (32 16 42 7)
(18 41 46 30) (12 42 39 34) (47 28 15 37) (23 1 10 38) (7 13 24 22) (40 25 11 4) (5 48 3 19) (36 35 31 21) (20 16 27 9) (14 32 44 45) (2 6 29 26) (33 17 43 8)