The answer to this question is incredibly broad, but first it all comes down to what age group you mean when you say "child" , in my personal opinion influence in a child's life basically means those factors that shape the child's behavior and attitude , in the early years (age 0-7) the main influence in the child's life would be his immediate social environment of which his family is the main component, and every member of the family influences the child consciously or subconsciously.

The later years of a child's life would bring about exposure to other factors that further shape the personality of the child, factors like peer group influence in which case children adopt personalities and attitudes of those within their age group, who have in turn been influenced by members of their families in a situation I like to call "culture-mixing", and there is also mass media which exposes the child to different situations and circumstances that go a long way in structuring the child's perspective of the world, but the availability of mass media also depends on the child's social environment.

It's my opinion that there is no one individual or factor that holds total credit in influencing a child's life but rather the major influence in a child's life is his environment along with it's nature and content, but if asked to pick one as the BIGGEST influence I'd say it's the family, being the first agent of socialization that the child is exposed to and the one that has the highest emotional impact on the child.