It is difficult to give advice without knowing the exact number of players, so you should probably look for some software for tennis doubles. This is one free option (http://www.greencourtsoftware.com/demo/).
24 players would be a good number to schedule for. For example you could use the following:
(15 11 9 7) ( 2 8 22 24) (18 1 21 17) (16 10 4 5) (12 19 23 20) ( 3 6 13 14)
(13 12 7 8) ( 3 9 23 22) (16 2 19 18) (17 11 5 6) (10 20 24 21) ( 1 4 14 15)
(14 10 8 9) ( 1 7 24 23) (17 3 20 16) (18 12 6 4) (11 21 22 19) ( 2 5 15 13)
(17 19 7 14) (13 20 4 22) ( 3 15 12 21) ( 8 16 1 11) ( 5 18 24 9) (10 6 2 23)
(18 20 8 15) (14 21 5 23) ( 1 13 10 19) ( 9 17 2 12) ( 6 16 22 7) (11 4 3 24)
(16 21 9 13) (15 19 6 24) ( 2 14 11 20) ( 7 18 3 10) ( 4 17 23 8) (12 5 1 22)
where each round of 6 games could be split into 2 mini rounds played on the 3 courts available to you. No matter how you assign each group of 4 players to
2 vs 2, you will always end up with each player having 6 different partners, and 12 different opponents, with no overlap between partners and opponents.
If there were only 2 courts available, you could just use the first four rounds, splitting each in to 3 mini-rounds.