The answer may surprise you.
For an adult, you need to push one and one half to two inches deep.
For a child, you need to push one third to one half of the front-to-back thickness of the chest at the nipple line.
Let's examine two examples: if a child's chest is six inches thick, you will be pushing anywhere from two to three inches - deeper than you would push on an adult's chest. If the child's chest were nine inches thick, you would be pushing three to four and one-half inches deep.
Bob