I've never played in a co-op tournament myself, but...
I think that victory could be time-based. Each player would have to bring an Imperial deck with a pre-determined structure (either using the standard core set composition, or with explicit card-for-card replacements) and a Rebel deck (which could be customized). Random teams of 4 would be generated and they would play a game. There would be a time limit (30 min? 45 min? 1 hr?) and each player on a team would accrue the elapsed time to victory. Defeats would result in the full time limit being applied. Then, for rounds 2 and beyond, the teams would randomly generate again, with no two players being on the same team until they have played with everyone else.
At the end of the tournament, the player with the shortest aggregate time would be the champion, with 2nd, 3rd, etc. following.
This structure has the following weaknesses: (1) Unless there is a judge at each game (unlikely), this structure would rely on the honor system for fair and consistent gameplay, (2) Teams that ran out of time would be penalized just as much as teams that were actually defeated. Adding an additional penalty for defeats, however, would lead to teams sandbagging instead of risking a defeat, (3) While every player would be expected to bring an Imperial deck, only a fraction of those would actually be used. However, it is unreasonable to expect that a store or a tournament coordinator will be able to supply these cards independently, (4) This structure could lead to coordinated manipulation of the standings. For instance, a group of 4 friends could go to a tournament and determine that Player A will win it. Then, Players B, C, and D would purposefully draw-out their games when they are NOT teamed with Player A, thereby manipulating the rankings.
Feel free to point out any additional holes in this argument. I am just throwing this out there based on what I have seen in my PvP tournament experience.