Modified Round Robin Tennis Tournament

[smckenzie04]

I am taking over a doubles tennis tournament with a group of 12 guys we have each year and in the past they would assign everyone a card and the order picked seeds the session. The problem becomes when partners and matches repeat more than whats required, which would be playing with everyone twice and two people 3 times (11+11+2=24).
We play 3 sessions of 8 matches each, totaling 24 matches per person. I would like a way to randomly pick who each person plays with and also who you play against as much as possible.

The following picture is what I have set up so far but its simply a modified round robin schedule and the order you play with your partners doesn't vary. I would appreciate any help to make it truly random.

 

[smckenzie04]

I'm going to revive this in an attempt to make it work now that I have more than two weeks the event.

For simplicity sake I want everyone to play WITH each person twice. I would LIKE to evenly distribute the number of times you play AGAINST each person as much as possible but that's a secondary concern at this point.