In order to buy life insurance on another person there must exist an "insurable Interest" in the person.
Insurable interest means you rely on another person for some form of financial support.
Since your child's father is responsible for child support, you do rely on him for financial support, and you are eligible to buy a life insurance policy on him.
However, you will need his permission, signature on the application, and he may need to answer some health questions, and possibly have to take a physical exam for the life insurance.
Some people make life insurance a part of their divorce settlement agreement, requiring the father to have life insurance naming the ex-spouse as beneficiary of the life insurance policy so the ex-spouse can manage the money from the life insurance for the child until the child is a legal age.