Make a backup of the FaceGeom mesh!
Do not close the instance of NifSkope with the source EyesFemale.nif! The copied info is not stored in the clipboard, so the source instance of NifSkope needs to remain open until you've finished.
1. load a working EyesFemale.nif into NifSkope. I obtained one by scavenging it from Skyrim - Meshes0.BSA using BSA extractor.
2. locate 5-NiSkinPartition and highlight it (5 is the correct index for a vanilla SE EyesFemale.nif)
hint: click the eye mesh in render view to highlight the correct BSTriShape
BSTriShape > NiSkinInstance > 5 NiSkinPartition
3. right-click 5-NiSkinPartition and select Block > Copy
4. load the FaceGeom mesh with dodgy eyes into another instance of NifSkope
5. click on the dodgy eye mesh (not the headmesh itself) in the render view (this will select its parent BSTriShape) and locate its NiSkinPartition by expanding the branches
BSTriShape > NiSkinInstance > NiSkinPartition
6. highlight the NiSkinPartion, right-click and choose Block > Paste Over (not Paste!!!!).
7. hopefully the dodgy eyes are now fixed and you can save the mesh!
8. don't be alarmed if NifSkope asks if you want to save the source EyesFemale.nif when you try to close it. Copying for some reason makes NifSkope think the mesh has been changed.
I can't explain the procedure any clearer than that, sorry! Good luck