Here is the standard Whist schedule for 9 players, it is doubles play where all possible partners occur once and all opponents twice. The schedule has 9 rounds so you will need to generate 4 variants, each time making a different random assignment of the letters A to I to your 9 players. Finally delete one of the 36 rounds to give a schedule for 35 weeks.
(B C) v (D G) (E I) v (F H) (A)
(C A) v (E H) (F G) v (D I) (B)
(A B) v (F I) (D H) v (E G) (C)
(E F) v (G A) (H C) v (I B) (D)
(F D) v (H B) (I A) v (G C) (E)
(D E) v (I C) (G B) v (H A) (F)
(H I) v (A D) (B F) v (C E) (G)
(I G) v (B E) (C D) v (A F) (H)
(G H) v (C F) (A E) v (B D) (I)
Hope that helps.
Ian.