You are organizing a Speed Dating event for bisexual people interested in dating either men or women. You are offering a special twist on the standard idea of how Speed Dating is done:
Men and women are rotated to meet each other over a series of short "dates", usually lasting from 3 to 8 minutes depending on the organization running the event. At the end of each interval, the organizer rings a bell, clinks a glass, or blows a whistle to signal the players to move on to the next date. At the end of the event players submit to the organizers a list of who they would like to provide their contact information to. If there is a match, contact information is forwarded to both parties. Contact information cannot be traded during the initial meeting, in order to reduce pressure to accept or reject a suitor to his or her face.
--Speed dating - Wikipedia, the free encyclopedia
Since each of your players are ready to date either men or women, you offer them the chance for a "date" with every other player.

At the start of the event, you give each player a sheet of paper indicating which table they are to go to for their date. For example, if you had only four players, their sheets would look like this:

Person #1:
Round #1: Table #1 for date with person #2
Round #2: Table #1 for date with person #3
Round #3: Table #1 for date with person #4

Person #2:
Round #1: Table #1 for date with person #1
Round #2: Table #2 for date with person #4
Round #3: Table #2 for date with person #3

Person #3:
Round #1: Table #2 for date with person #4
Round #2: Table #1 for date with person #1
Round #3: Table #2 for date with person #2

Person #4:
Round #1: Table #2 for date with person #3
Round #2: Table #2 for date with person #2
Round #3: Table #1 for date with person #1

How can you quickly produce sheets like this for any given (even) number of players?

The formula must produce every possible coupling of all players, each at a unique round and table of the game. The number of tables will be one half the number of players, the number of rounds will be one less than the number of players.