I'm participating in the creation of an archery club, and we want name it dragon's archers in Latin. The Google Translate result draco sagittariis doesn't convince me. I think the declination is not correct. I bet for sagittarii draconis.
It could be just "Dracōnēs sagittāriī"
If you mean Dragon's Archers/Archers of the Dragon it would be "Dracōnis sagittāriī"
Or if you mean Dragons' Archers/Archers of the Dragons it would be "Dracōnum sagittāriī".
Note: both terms of any of those three sentences may be used in whichever order you like.