I was sure that there was going to be a solution to the all-play-all movement somewhere in the computer science literature. However, there doesn't appear to be any direct work done to solving the problem.
There are a few timetabling problems that relate and it could well be like the Travelling Salesman problem unless you know its name it is difficult to find.
Anyway, since I was probably only going to need small numbers I decided that I would just settle for a simple computer program.
To find the possible combinations without overlaps for 3 players a round wtite down all of the numbers in combinations of pairs to form a triangle
e.g.
12
13 23
14 24 34
15 25 35 45
....
Then to find a combination you just make an L or triangle with three points and cross them out. With four players you will have 6 to cross out. Not solved the problem for diplomacy a 7 player games.
Unfortunately, the elegance of the 9 players 3 at table is not repeated for larger numbers
ie
123 456 789
168 249 357
147 258 369
159 267 348
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