The deciding factor for insurance companies on whether you can take out a life insurance policy on a person is known as "insurable interest." Before an insurance company will allow you to take out a life insurance policy on a person, you must be able to show that the person's death would have an adverse affect or the listed beneficiary. Since the death of the child's father could impact support payments, health insurance, or even household necessities such as room and board, the insurance company may recognize a definitive insurable interest and allow you to take out a life insurance policy on the father even if you are not married.
If your cannot get an insurance company to agree to allow a life insurance policy, your next recourse is to go through legal avenues. A judge may agree with you that the death of the father would create unnecessary hardships and require such a policy. A court ordered life insurance policy may be very limited, however, such as guaranteeing the continuation of child support payments even if the father passes away, but no lump sum payout. Before you attempt to go through the courts for life insurance, talk with several different insurance agents and find out why they are denying the policy and what suggestions that can offer you to solve the problems.