I just noticed a cut on my 9 mo old eyelid. It happened with the babysotter so I don't know how. Its not bleeding. Can I put neosporin there?

Yes. Wash the area with soap and water, put neosporin on it, and make an appointment with an eye doctor. Eyelid cuts may be superficial and heal well, but if they are deep, they should be tended to promptly. If you are unsure how severe the cut is or if there is a lot of swelling and tenderness, go to an emergency room rather than wait a day.
No neosporin. I would just wash it with soap and water and keep it clean. I would not use neosporin. If it becomes red or has pus then i would have the baby seen by the doctor.