You may also want to inspect your printer color management. Does it allow change of saturation?
You already noticed that the colors are partly to blame to camera model. I have a feeling that some Sony cameras may be a tiny bit too enthousiast with green and this is exactly a problem color for printers; Monitors RGB (Red Green Blue) and printers are CMYK (Cyan, Magenta, Yellow, Black). Thus the green any camera produce is translated to the printer into a mixture of Yellow, Cyan and Black...
Again if your printerdriver software allows user profiles with settings like color balance and saturation, you may like to create a special profile for the camera.