Can you get life insurance for your child's father if you are not married?
Yes you can. To get insurance, insurance companies, want to see an "insurable interest." Since he is the father of your child, you have an insurable interest on him.
A son can not generally take life insurance policy on his father's life because of lack of insurable interest in the life of father. Life insurance works on the principle of insurable interest. A father generally has insurable interest in the life of his child due to emotional reasons. That is why life insurance companies design the products for the children which take care of their education and other expenses once they grow up.
It's like finding out a needle from a heaps of straws ! It's advisable that you contact local branch office of your Life Insurance Company, if they can help you to find out about existence of a life insurance policy of your dead father. Searching by name/address of your dead father over Net may be beneficial.