No, that's not.
It is impossible to change eye color expect for surgeries or diseases. The color of our eyes is decided by the amount of melanin inside the iris stroma which has been predetermined by genes and hereditary. The short or long wave lengths of sunlight which enters our iris are either absorbed or reflected by the melanin inside. Light colored eyes have little melanin, so most wave lengths are reflected, leaving blue eye color. This is the same as how we see the sky is blue. Only surgeries and diseases can change the amount of melanin inside the iris.
Therefore, taking honey every day won't change eye color.
Usually drinking honey daily will keep your eyes moisture and make your eyes become bright. However your eye color will not change. Usually the eye color is determined by the genetic genes which will not change easily. If there is the change in your eye color, you may pay attention to the health of your body. Commonly the healthy problems will cause the eye color change.
Well, no, in my opinion, honey cannot change eye color. For our eye color, you should know that we are born with certain eye color. And in common, it will not change with time. But on the other hand, some reports have shown that weather and emotion can just change eye color temporarily. But there is no evidence which has reported that honey can have the same effect. But honey can be good for your eyes. As we know that honey is a natural sweetener and its incredible antiseptic, antioxidant and cleanser of our system. And honey can do a good job to the eye infection and the pink eyes. Also, black eyes and dark circles under eyes can be treated with honey too.