I was married but separated when me and my new husband had our 2 kids. So, in South Carolina, the husband, even if separated, is legally the father, and is suppose to be listed on their birth certificates. I refused to give his info so their certificates say father unknown. How do we get it changed so that my new husband, the biological father, is legally their father?

He needs to file for paternity and ask for a test in court.
The issue that you were married, is a fact of law and easy to date against birth. So he would be contacted to sign away his legal rights to allow the adoption

By law, when a child is born to a married couple the husband is legally the father. Some states have a very limited window on how long this can be challenged.

You need to hire an attorney to get this straightened out. Either you mount a challenge to paternity getting DNA tests to prove paternity or your current husband adopts the kids.