When a child is too young to say the bed-time Shema for himself, the custom is that parents say it for them as they go to bed.
Should the parent cover their own eyes, the child's eyes, or perhaps neither (or both, but I assume not)?
As I recall from when my children were the age you imply (40 years ago) I would cover my eyes and the child would imitate me by covering his or her own eyes. Since they were learning by saying it with me, it was part of teaching them. I do not recall a specific psak. It did not take long for them to learn what to do.