Keith,

It isn't possible for each foursome to be completely different.

There are 1770 different pairs of people that can be made from a group of 60.

Every foursome accounts for 6 different pairs of people. Each week you'd have 15 foursomes. That makes 6 x 15 = 90 pairs of people who have played together in a given week. Over 24 weeks that means 24 x 90 = 2160 pairs of players have played together.

Since 2160 > 1770, some pairs of people must play together twice.

What you might consider doing is breaking your 60 players in to a group of 32 and a group of 28, and then scheduling each group for 9 weeks using the schedules at http://www.maa.org/editorial/mathgames/mathgames_08_14_07.html. To get the next 9 weeks, break the group up differently and do the same thing, and so on.

Good luck!
Victoria