Unfortunately I can only see solutions for 14 or 15 teams. Any higher and managing the multiple byes becomes a problem, any less and arranging that every team plays all the other teams at least once becomes a problem.
For 14 teams use the following schedule:
(A B) (C D) (E F) (G H) (I J) (K L) (M N)
(G D) (E M) (L A) (J N) (C H) (I F) (K B)
(I M) (L N) (K J) (B C) (F G) (D A) (E H)
(L C) (K F) (H I) (D E) (B M) (G N) (J A)
(J E) (B I) (C N) (A F) (D K) (H M) (L G)
(N F) (A H) (G B) (M K) (E L) (J C) (I D)
(K H) (J G) (D M) (I L) (A N) (E B) (F C)
(H F) (D J) (I E) (N K) (C M) (L B) (A G)
(G E) (C I) (F J) (M L) (N D) (K A) (B H)
(A I) (H N) (G K) (B D) (L J) (M F) (C E)
(B J) (M G) (H L) (A C) (K I) (N E) (F D)
(D L) (E K) (M A) (J H) (F B) (G C) (N I)
(C K) (F L) (N B) (I G) (E A) (H D) (M J)
(M N) (A B) (C D) (E F) (G H) (I J) (K L)
The 7 columns above are the events and there are 14 rounds. Note that the 14th round repeats the same pairings as the 1st round, and these are the only pairings that occur twice.
For 15 teams, use the 'schedules' button near the top of this page, bring up the cyclic round-robin for 16 items, throw away the 1st 'match 1' column, leaving a schedule for 15 teams (numbered 2 to 16).
