What hair products should I avoid for my child who has greasy scaling of the scalp?

Chemicals. Avoid harsh soaps, shampoos and detergents. Use anti-dandruff shampoo (selsun blue, head and shoulders, neutrogena t/gel) 2-3x/week. Your doctor may also prescribe an antifungal shampoo (nizoral).
Cradle cap. Greasy scaling of the scalp may be a type of seborrhea or eczema, often called cradle cap, or a form of psoriasis. In general, use products for sensitive skin, avoid heavy oils or heavy fragrances. Ask your pediatrician for advice, in some cases, medicated shampoos or prescription lotions may be used.