Rotating 2v2 Tournament Brackets HELP!!!

A group of my friends and I want to create a 2v2 round robin style tournament where every week is a new match, and the teams rotate as well (so for instance in a match in week 1, players A and B play players C and D. Then next week players A and F play players B and H, etc.) The goal is for every player to be able to play a good spread WITH every player and AGAINST every player. We have 8 players in the tournament.

The problem is that the number of possible permutations is simply too high if we wanted to play every combination. We are having trouble coming up with a suitable bracket so that every player plays a similar number of combinations (for instance, we dont want player A playing with player B 8 times, while only playing with player C once, but if he plays with B 4 times and C three times, thats ok).

Basically, if any math geniuses or tournament junkies have any idea how we could set up the brackets to keep the tournament relatively short (a 21 round tournament would be ideal IMO, something around there), while at the same time allowing a good spread between every group, I would love to see how it could be done!

We have a scoring system and rules ready, we simply need a way to match up players each week that is fair and consistent.

Any help would be greatly appreciated!