Answer:
A parent can obtain life insurance for and on their minor child(ren). This is because a parent is deemed to have an insurable interest in the life of the child based upon "natural love and affection".
Most states do not have restrictions on obtaining life insurance for a child, although there are some exceptions to this general rule. The safest avenue, therefore, is to consult a licensed life insurance agent or broker in the state in which the policy will be issued (delivered).
Different life insurers have different underwriting guidelines, so it is generally best to have the agent or broker shop the market to determine available companies, premium structures, and related factors.