It's possible to have as many as 9 rounds at which point every team will have been
placed in a division with all 63 other teams exactly once.
In mathematical terms you need to construct an order 8 affine plane, see here for diagrams of the order 2 and 3 planes (http://en.wikipedia.org/wiki/Finite_geometry). For the construction itself you will need to use a Galois Field. Each line connects all the teams in one division and each set of 'parallel' lines forms one round.
It should be possible to copy/paste the schedule below on to an Excel worksheet and then use a fixed width 'Text to Columns' on it to get 10 separate columns of numbers.
Hope that helps.
Round Div Teams
1 1 ( 1 2 47 11 12 38 48 37)
1 2 ( 3 4 45 9 10 40 46 39)
1 3 ( 5 6 43 15 16 34 44 33)
1 4 ( 7 8 41 13 14 36 42 35)
1 5 (17 18 63 27 28 54 64 53)
1 6 (19 20 61 25 26 56 62 55)
1 7 (21 22 59 31 32 50 60 49)
1 8 (23 24 57 29 30 52 58 51)
2 1 ( 1 64 42 3 62 21 23 44)
2 2 ( 2 63 41 4 61 22 24 43)
2 3 ( 5 60 46 7 58 17 19 48)
2 4 ( 6 59 45 8 57 18 20 47)
2 5 ( 9 56 34 11 54 29 31 36)
2 6 (10 55 33 12 53 30 32 35)
2 7 (13 52 38 15 50 25 27 40)
2 8 (14 51 37 16 49 26 28 39)
3 1 ( 1 45 56 32 52 5 28 41)
3 2 ( 2 46 55 31 51 6 27 42)
3 3 ( 3 47 54 30 50 7 26 43)
3 4 ( 4 48 53 29 49 8 25 44)
3 5 ( 9 37 64 24 60 13 20 33)
3 6 (10 38 63 23 59 14 19 34)
3 7 (11 39 62 22 58 15 18 35)
3 8 (12 40 61 21 57 16 17 36)
4 1 ( 1 55 50 58 16 63 8 9)
4 2 ( 2 56 49 57 15 64 7 10)
4 3 ( 3 53 52 60 14 61 6 11)
4 4 ( 4 54 51 59 13 62 5 12)
4 5 (17 39 34 42 32 47 24 25)
4 6 (18 40 33 41 31 48 23 26)
4 7 (19 37 36 44 30 45 22 27)
4 8 (20 38 35 43 29 46 21 28)
5 1 ( 1 15 17 14 4 20 31 30)
5 2 ( 2 16 18 13 3 19 32 29)
5 3 ( 5 11 21 10 8 24 27 26)
5 4 ( 6 12 22 9 7 23 28 25)
5 5 (33 47 49 46 36 52 63 62)
5 6 (34 48 50 45 35 51 64 61)
5 7 (37 43 53 42 40 56 59 58)
5 8 (38 44 54 41 39 55 60 57)
6 1 ( 1 61 59 29 33 27 7 39)
6 2 ( 2 62 60 30 34 28 8 40)
6 3 ( 3 63 57 31 35 25 5 37)
6 4 ( 4 64 58 32 36 26 6 38)
6 5 ( 9 53 51 21 41 19 15 47)
6 6 (10 54 52 22 42 20 16 48)
6 7 (11 55 49 23 43 17 13 45)
6 8 (12 56 50 24 44 18 14 46)
7 1 ( 1 13 46 26 22 57 34 53)
7 2 ( 2 14 45 25 21 58 33 54)
7 3 ( 3 15 48 28 24 59 36 55)
7 4 ( 4 16 47 27 23 60 35 56)
7 5 ( 5 9 42 30 18 61 38 49)
7 6 ( 6 10 41 29 17 62 37 50)
7 7 ( 7 11 44 32 20 63 40 51)
7 8 ( 8 12 43 31 19 64 39 52)
8 1 ( 1 36 10 25 60 51 43 18)
8 2 ( 2 35 9 26 59 52 44 17)
8 3 ( 3 34 12 27 58 49 41 20)
8 4 ( 4 33 11 28 57 50 42 19)
8 5 ( 5 40 14 29 64 55 47 22)
8 6 ( 6 39 13 30 63 56 48 21)
8 7 ( 7 38 16 31 62 53 45 24)
8 8 ( 8 37 15 32 61 54 46 23)
9 1 ( 1 54 35 40 19 49 24 6)
9 2 ( 2 53 36 39 20 50 23 5)
9 3 ( 3 56 33 38 17 51 22 8)
9 4 ( 4 55 34 37 18 52 21 7)
9 5 ( 9 62 43 48 27 57 32 14)
9 6 (10 61 44 47 28 58 31 13)
9 7 (11 64 41 46 25 59 30 16)
9 8 (12 63 42 45 26 60 29 15)