If the child support that was reported on your credit report is in active collections and you still owe that child support then no you cannot get that child support removed from your credit report.
You would have to pay off the child support first in full and then proceed with the proper paperwork and contact the credit bureaus to get the child support remark removed from your credit report.
You have to prove to the credit bureaus that you've paid off the child support in full for them to remove the child support reported on your credit rating.
However if it's been over 7 years since they last tried to collect the child support and they haven't tried to take you to court or sue you for the child support owed then the report of the child support should affect your credit score after 7 to 10 years.