If Cherno has her first Manifestation, then giving her a strong healer can allow her to sustain her ult for much longer, massively increasing her dps.
As such, Eatchel - The Cub and Yao- Quiet Quitter are great supports for Cherno, and Chenxing - The Observer is also quite good.
As a main dps Cherno spends a lot of time in combat shooting stuff, so ballistic and per-shot buffs work well, such as Tess - Phantasia and Fritia - Little Sunshine.
Since a lot of damage comes from her standard and ultimate skill, skill damage buffs such as Siris - Freefin, Marian - Riptide, and Chenxing - The Observer work well with her.
Operatives that can reduce enemies chaos damage resistance such as Vidya - Celestial Swan, Acacia - Kaguya, or Marian - Queen of Pain also work well with Cherno.
If you only have 4* operatives to support Cherno, then her best support is Fritia - Little Sunshine, who adds Thermal damage to each shot.
From there you will likely want a healer, so take Yao - Quiet Quitter.
As a support, Cherno is a very generic support, providing Slow, damage taken debuffs, and ATK buffs, which can be used by basically all dps operatives.
As such, she can be used to support basically any operative, although she isn't a particularly strong support.