Which rider provides a specific amount of coverage for the children of the insured?

The children's term rider is designed to provide a specific amount of life insurance coverage for the children of the insured. This rider allows parents to add a predetermined death benefit for each child to their life insurance policy, ensuring that any financial burden resulting from the loss of a child is alleviated. Typically, the coverage under a children's term rider is available until the child reaches a certain age or until the policyholder chooses to convert or terminate the rider.

This option is particularly beneficial for parents as it provides peace of mind knowing that their dependent children are covered without necessitating a separate policy for each child. In contrast, the other riders mentioned do not specifically provide protection for a child’s life.

The accidental death benefit rider, for instance, extends coverage in the event of an accidental death but does not specifically address children. The cost-of-living rider adjusts the policy's benefits according to inflation but isn't related to coverage for children. Lastly, the return of premium rider allows for the return of premiums paid if the insured outlives the term of the policy, which again does not pertain to child coverage. Thus, the children's term rider stands out as the correct choice for providing specific life insurance coverage for the children of the insured.