The answer to that question is "almost anyone."
A person may be limited in the amount of their contribution if their modified adjusted gross income exceeds a certain amount. For income limits refer to the section titled "How much can I contribute."
The ESA does not specify that the contributor must be a member of the family. With this broad range of potential contributions, it is possible that more than one person may want to contribute for the same child. However, there is a limit of $2000 per child per year no matter the number of people who plan on contributing. Therefore, a coordinated effort should be encouraged to avoid excess contributions.