Lee,
You don't say how you would like to arrange the players for each round. If you want foursomes then the situation is ugly, you will have to have a few pairs of players that play together in three out of the four rounds. For example see my response to a similar request.
An alternative comes from considering how to schedule 9 players. Here the most natural thing to do is to play three threesomes in each round like this,
Round 1: (5 4 2) (1 3 8) (7 9 6)
Round 2: (1 2 7) (4 8 6) (3 5 9)
Round 3: (6 1 5) (3 7 4) (8 9 2)
Round 4: (2 6 3) (5 8 7) (9 4 1)
This is an analog of Richard's Social square since every player plays with every other exactly once. Now remove the 9th player from the schedule to give
Round 1: (5 4 2) (1 3 8) (7 6)
Round 2: (1 2 7) (4 8 6) (3 5)
Round 3: (6 1 5) (3 7 4) (8 2)
Round 4: (2 6 3) (5 8 7) (4 1)
These mixed rounds of two threesomes and a pair are the only way to shedule the 8 players so that they all play together exactly once.
Ian.