The total number of byes must be 30, or 3 byes per player, so the total number of games per player is 12. But with 12 partners, and 24 opponents your criteria must be exceeded, otherwise it is possible to construct a suitable schedule. For example:
Court 1 Court 2 Byes
(7 2 v 9 6) (3 5 v 1 10) (4 8)
(8 3 v 10 7) (4 1 v 2 6) (5 9)
(9 4 v 6 8) (5 2 v 3 7) (1 10)
(10 5 v 7 9) (1 3 v 4 8) (2 6)
(6 1 v 8 10) (2 4 v 5 9) (3 7)
(1 9 v 3 2) (4 6 v 7 10) (5 8)
(2 10 v 4 3) (5 7 v 8 6) (1 9)
(3 6 v 5 4) (1 8 v 9 7) (2 10)
(4 7 v 1 5) (2 9 v 10 8) (3 6)
(5 8 v 2 1) (3 10 v 6 9) (4 7)
(9 3 v 4 7) (5 2 v 10 6) (1 8)
(10 4 v 5 8) (1 3 v 6 7) (2 9)
(6 5 v 1 9) (2 4 v 7 8) (3 10)
(7 1 v 2 10) (3 5 v 8 9) (4 6)
(8 2 v 3 6) (4 1 v 9 10) (5 7)
Everyone has at least 3 games between byes and plays 6 times on each court.
Hope that helps.
