How long does it take homeopathic medicine to cure amblyopia?

Never. There is no homeopathic treatment for amblyopia. Please challenge anyone claiming there is any type of "medicine" for amblyopia to produce a peer-reviewed published study demonstrating such a benefit from any medication. Then, let me know, because i would love to read it.
See ophthalmologist. Amblyopia is not a situation in which homeopathy alone is curative or appropriate. Certain ophthalmology procedures are needed in such cases, and time is of the essence so that the child's eyes can recover as much as possible. This doesn't mean that homeopathy isn't useful for the child's overall health -- but additional medical treatments are important in cases like this. Please use them.
Amblyopia. I've never heard of a product that cures amblyopia. Amblyopia is a condition where one did not develop the brain pathways and connections from when they were an infant. This is caused by poor vision in one eye (caused by many things) that was never corrected. Once you're over the age of 7, it's very difficult to improve it. Patching the good eye works when young, but not usually when you're older.