For a 9-team league, you can simply run 12 games every night, using the 9-team tournament grid; perhaps using slightly shorter games. But you might want to run 9 games every night, in which case a suitable grid is shown below. It takes 4 weeks to play.

12 games are played by each team.
36 games are played in the whole tournament.
Each team plays every other team 3 times.

Game
A1B1C1D1E1F1G1H1J1 A2B2C2D2E2F2G2H2J2 A3B3C3D3E3F3G3H3J3 A4B4C4D4E4F4G4H4J4
Team 1R G Y R Y G R G Y G Y G
2G Y R Y G R R G Y Y G R
3 Y R G R Y G R G Y R R Y
4Y R G Y G R R G Y G Y G
5 R G Y G R Y Y R G Y G R
6 G Y R Y G R Y R G R R Y
7 Y R G G R Y G Y R G Y G
8 Y R G Y G R G Y R YG R
9 R G Y G R Y G Y R R RY

The following would be a good shuffle rule:
1 to 2, 2 to 4, 3 to 6, 4 to 8, 5 to 1, 6 to 3, 7 to 5, 8 to 7, 9 to 9.

9 team tournament grid
8 team League Grids 10 team league