Can I put in my agreement that my estate would be responsible for child support payments should I decease?

Yes, you can agree to this in a separation agreement or child support agreement. In most states it is also required that the parent paying child support must take out a life insurance policy of at least $100,000 in order to provide support should he or she die. An insurance clause can be included in a separation agreement as follows:

The parties agree, that as long as child support payments are court ordered, the husband will carry and maintain life insurance in the amount of $100,000 naming the child(ren) as sole irrevocable beneficiary(ies). The parent obligated to provide such insurance will provide the other parent with annual proof of such coverage.