Is this not the same format as Whist? If you haven't seen them already, then click on the "schedules" link above, select Whist and then choose 16 players. Adjacent pairs of matches become the four players at each table, so Table 1 would be the two players in Match 1 partnered against the two players in Match 2. Table 2 would be Matches 3 & 4, etc. I know this doesn't give you everything you ask for, but if you were prepared for one player (16) to remain at the same seat, then all the other 15 would rotate through all other seats at all tables. Alternatively you could randomize the table assignment for each round.
I think you are asking for at least 12 rounds below, but if you can manage the full 15 of the Whist schedule then everyone will partner everyone else once and oppose each other twice.
Ian.
PS I have moved your message here as replies to threads in the guestbook are not possible.