Open Gm tuning
The open Gm tuning also known as Cross-note G tuning is not as common as the Open G tuning.
To get the open G minor tuning on your guitar you tune it like this: DGDGBbD. The strings that differ from the standard should be turned so the string tension is decreased and not the opposite.
Including an octave perspective, the tuning is written D2-G2-D3-G3-Bb3-D4, meaning that the lowest string is a D note on the second octave, the second lowest string is a G note on the second octave and so on. Standard tuning reference: E2-A2-D3-G3-B3-E4.
The Cm chord is more correctly written as Cm/G. By also include the open low e-string it would be a Cm/Eb.
The Cm chords is more correctly written as Dmadd11. A regular Dm chord could be played as xx0243 or 0x0243.
The Ebmaj7 chord could also be played as 100000 or 100001. The Eb9 chord is more correctly written as Eb9/D. Ebmaj9/D could be played as 000343.
The Fadd9 and F9 chords are more correctly written as Fadd9/D and F9/D. F7/D could be played as 021223 or 020553.
Other chord possibilities in Open G minor tuning:
Two chord progressions in this tuning:
Gm9 – Ebmaj7 – Bbmaj7 – Gm7
Gm7 – Dm – Cm/D – Bbmaj7
Open Am tuning
Another option is the Open Am tuning, which you can play in by putting a capo on the second fret when your guitar is tuned to Open Gm. Otherwise, the tuning for Open A minor is this: EAEACE. It can also be an advantage to use a capo compared to tuning in this case since two of the strings will increase the tension, which can result in breakage of the strings.
See also Open Dm tuning