As the schedule above was intended for golf foursomes, there is no accounting for the two-against-two format of doubles tennis. You may not have seen this as a problem since very few pairs of players play together twice, or in other words, most of the 6 partners and 12 opponents that a player has are different and it doesn't matter too much how you assign people as partners and opponents. With 12 rounds of play however, most pairs of players have the opportunity to meet twice and it will be essential to consider the two-against-two format, if you want to avoid having repeated partnerships and maximise the number of player pairs who meet once in partnership and once in opposition.
One way to procede would be to take part of a Whist Schedule. For example, follow the schedules link above, click on Whist, and then on 20 players to get a plan for a 19 round tournament where pairs of players meet exactly once in partnerhip and exactly twice in opposition. So one strategy would be to take the first 12 rounds of this schedule, this certainly solves the problem of giving each player 12 different partners, but when you look in more detail there are undesirable features - 5 pairs of players never meet (for example player 4 never meets player 3 or player 5), there are also 56 pairs who meet only once, and 46 pairs who meet three times.
It is possible to do much better if a schedule is designed specifically for a 12 round tournament rather than cutting down the Whist schedule. I have done this in the plan below, where all the partnerships are different, all pairs of players meet at least once, specifically 24 pairs meet once, and 4 pairs meet three times. There is very little room for improvement, that is elimination of the four pairs who meet thrice, so the schedule is close to anoptimal solution.
( 4 9 v 8 3) (13 10 v 12 20) (19 18 v 14 1) ( 5 15 v 17 6) ( 7 11 v 16 2)
( 1 10 v 5 4) (14 11 v 9 17) (20 19 v 15 2) ( 6 16 v 18 7) ( 8 12 v 13 3)
( 2 11 v 6 1) (15 12 v 10 18) (17 20 v 16 3) ( 7 13 v 19 8) ( 5 9 v 14 4)
( 3 12 v 7 2) (16 9 v 11 19) (18 17 v 13 4) ( 8 14 v 20 5) ( 6 10 v 15 1)
( 5 3 v 6 13) ( 1 19 v 2 17) (20 4 v 11 15) (14 12 v 8 7) (10 9 v 16 18)
( 6 4 v 7 14) ( 2 20 v 3 18) (17 1 v 12 16) (15 9 v 5 8) (11 10 v 13 19)
( 7 1 v 8 15) ( 3 17 v 4 19) (18 2 v 9 13) (16 10 v 6 5) (12 11 v 14 20)
( 8 2 v 5 16) ( 4 18 v 1 20) (19 3 v 10 14) (13 11 v 7 6) ( 9 12 v 15 17)
(17 10 v 2 14) (19 6 v 20 8) (13 16 v 4 15) ( 5 11 v 18 12) ( 1 9 v 7 3)
(18 11 v 3 15) (20 7 v 17 5) (14 13 v 1 16) ( 6 12 v 19 9) ( 2 10 v 8 4)
(19 12 v 4 16) (17 8 v 18 6) (15 14 v 2 13) ( 7 9 v 20 10) ( 3 11 v 5 1)
(20 9 v 1 13) (18 5 v 19 7) (16 15 v 3 14) ( 8 10 v 17 11) ( 4 12 v 6 2)
