It is not clear exactly why you want to "improve" your child's skin. You have not mentioned any real skin condition or symptoms, and the only problem you seem to have is that the color of your child's skin is not light enough. Dark skin is not something that needs to be improved, and trying to do so can unnecessarily damage the skin. However, in addition to the physical harm, you will also cause emotional and psychological harm to your child by damaging his or her self image, and unnecessarily introducing concerns that children are best left without. You will end up teaching your child that he or she is not good enough the way he or she is, and all this for something that is not even within the child's control, or even within your control.
Skin color is determined by one's genes, and it is impossible to lighten one's skin. All skin contains melanocytes, which are special cells that produce the pigment melanin, but one's genes determine the amount of melanin that these cells produce. The more melanin there is in the skin, the darker is the skin color, and vice versa. There is absolutely nothing wrong with having more melanin in one's skin, and in fact, light skin has the disadvantage of being more susceptible to damage from ultraviolet light. Melanin protects the skin against ultraviolet light, and therefore people with dark skin have a lower risk of developing skin cancer due to excessive exposure to sunlight. As far as beauty goes, concepts of beauty vary widely across the world and across cultures, but many people all over the world and in all cultures see no correlation between fairness and beauty.
What is more important than the color of the skin is its quality - dark skin that glows will certainly look much better than fair skin that is dull and dry. Usually, children naturally have excellent skin, but if you feel that your child's skin looks dry or dull, you should first of all look at your child's diet and water intake. Make sure that your child drinks at least 8 glasses of water a day, and possibly much more if he or she is athletic, and ensure that his or her diet is healthy, with a wide variety of fruits and vegetables, and minimal junk food. If these factors are taken care of and your child still has bad skin, you should consult a doctor.
answered by M W