ISO My Husband's possible child- Tallahassee area birth 87-89

Husband was living with a women named Valerie in the Tallahasse area in the late 80's. She became pregnant and left my husband. Some months later, she gave birth to a child and placed it for adoption. She was with another man at that point, but the timing matches when she would have been pregnant by my husband. Birthmom denies ever having been pregnant of having a child during that time, but my Hubs was there when she found out about the pregnancy and he even spoke to my FIL about it for advice, so we KNOW she was pregnant. I need to get the exact year, but baby, who we believe is female, was born between 1987 and 1989. This is tearing my husband to pieces that there is a child out there that might be his and he was never given an opportunity to be a father. He is going so far as to look for TV shows to solicit trying to find the child. We don't have the money to hire an attorney for searching. DH can't even remember birthmom's last name at the time, yet we have her married name now. Birthmom has older daughters also. DH and I have 2 little ones. We would love to find out 1- did she really give a child up for adoption and 2- does my DH have a child out there that he hasn't met. I am so sorry if this is out there, I am literally crying for my husband who cried himself to sleep last night over this.