I have an 18 month old son. His non biological father signed the birth certificate with out having a dna test done, now I don't know how to get him off the certificate and get the biological father on.

Contact the Vital Statistics office for whichever state your child was born in. They should be able to help you.

Were you married at the time the child was born?

Also where do you live, the bio father can contest the paternity in court and ask to be added to the birth certificate.
** but limited in some US states

ANY question on law needs to include your general locale as laws vary by area.

If someone signed an acknowledgment of paternity, they are the legal father unless a challenge can be mounted. The window of time for a challenge to be mounted depends on local law.

Contact the Vital Statistics office for whichever state your child was born in. They should be able to help you.

I do not think that the Vital Statistics office may help in that situation...
The only way is through the court system. The laws vary from state to state.