Don't know who father of child is

I am 25 years old and the mother of two children. After having one child, me and my husband got a divorce. After realizing I "grew up to fast", while either my mother or my ex husband had my first child, I was having fun with friends. One night in July of 2009, I was very much under the influence of alcohol when I slept with someone who was apparently a friend of friend. I have never seen this person before and this person, without the obvious evidence of my second child, seems to be a ghost because no one I know or talk to anymore has any idea of who that person was, not even a name.

Needless to say my "partying" days are well over and I am a very responsible mother of two beautiful children. I receive public assistance in the form of help with child care costs for both of my sons and I am ordered to cooperate with child support enforcement. My ex husband is ordered to pay child support, in which he doesn't and hasn't in over a year. I, of course, can give information on him, but for my second child, in not knowing one clue as to who the father is, don't know what to do. Establishing paternity is not an option for him, so I don't know if that is considered not cooperating based on Colorado laws? What do I do?