For amblyopia, commonly known as "lazy eye," it is first recommended to take vitamin A and beta-carotene by eating fruits and vegetables along with fairly strong antioxidants such as blueberry, which is available in syrup form for children.
In addition, there is a mushroom called "hericium" that works very well for eye problems.
Furthermore, omega-3s, and especially fish oils available as dietary supplements, will be very beneficial.