Unfortunately for you, the IRS specificially states that "for purposes of calculating the earned income Credit, child support is not considered earned income".
IRS defines "Earned income" that is generally meant to be include wages, salaries, tips, other taxable employee pay, and net earnings from self-employment. Employee pay is earned income only if it is taxable.
Also, nontaxable employee pay, such as certain dependent care benefits and adoption benefits, is not considered earned income. But there is an exception for nontaxable combat pay, which you can choose to include in earned income.
Earned income is further explained in detail in Rule 7 in chapter 1 of Publication 596, Earned Income Credit.