I've seen a few people make their child drink alcohol when they have a cold. They believe that it can reduce the cold and cough. Is that true? If so, what is the right amount of alcohol the child can consume? In the case of my question, the child is 9 years old.
The right amount is none. Not at all. Don't do it. Don't even consider it.
There have been multiple studies on alcohol and brain development, quite a few of them on teens, as they are one of the higher risk groups. All of these show significant impacts on brain and social development. There are fewer on the young child (non infant) as they are not considered a risk group. More studies in that area look at the effect of the adults consumption around them.
However, studies such as this one on postnatal rats show that even a single day of alcohol exposure is enough to affect brain weight and development in the postnatal period. This study also suggests that once the brain is formed, and going through differentiation (The process by which cells become specialized for their various functions) alcohol has a greater impact than when it is forming in utero.
In short, children should not be given alcohol for any reason. There are now warnings about such medications as cough syrups to not use them for any children under 4, as well as warnings about alcohol in formulas for older kids. I encourage you to read the labels, and choose non alcohol formulas if you do choose to administer cough syrup.