Child is 10, and has earned income. Does the AGI limits apply to the child or the parents of the child since the child is still a dependent? The regs address earned income and maritial status.

The income limitation is based upon the child's income, not the parents. As long as the child has earned income and the child's income is within the limits, the child can have a Roth IRA.

Not all custodians will open an IRA for a minor. I know that Charles Schwab will.