There are no balanced doubles tournaments like this when the number of players is 4n+2, or 4n+3 (above you are asking about n=1). If you are willing to compromise then the following might work for 7 players:
(B D) v (F G)
(C E) v (A B)
(D G) v (B C)
(E F) v (A G)
(C F) v (D E)
(B G) v (A E)
(A F) v (C G)
(D F) v (B E)
(B F) v (A C)
(E G) v (C D)
Above the pair (A D) never play in the same game together and they have only 5 games while the other 5 players all have 6 games. Apart from the pair (A D) all other pairs partner once and oppose twice. I am not aware of anything similar for 6 players.
