Derek,

I’m not sure if this is what you want since it it not clear how many weeks there are in the season. Let’s try anyway:

First schedule the teams of six. There is a schedule where every 2 players have been partners exactly once. Here it is:

1. 12, 34, 56
2. 13, 25, 46
3. 16, 23, 45
4. 14, 26, 36
5. 15, 24, 36

Now use the schedule above to construct the matches involving the pairs from team A and team B. Schedule 1 (for each team) gives 3 weeks of golf (week 1 is 12v12, 34v34, 56v56, week 2 is 12v34, 34v56, 56v12, etc). After 3 weeks every pair among Team A 12, 34, 56 have played every pair from Team B 12, 34, 56. The same goes for Schedules 2, 3, 4, 5.

So, over 15 weeks you can have every pair from Team A against every pair from Team B exactly once. What I’d suggest is using week 1 from each schedule, then (after 5 rounds) week 2 from each schedule, then (after 5 more rounds) week 3. That way players on the same team are partners once every 6 weeks.

Hope this helps.
—Victoria