I have paid a debt in a court ordered judgement(small claims) . I understand that the person who filed the case has a time limit to file a satisfaction form with the courts. How long does this person have? And if my credit is affected for failure to do so. What are my recourses?

It would depend upon which state or country you are in. Rules vary from jurisdiction to jurisdiction.

The adverse affect upon your credit rating resulting from tardy filing of a satisfaction of judgment will be minimal. The big hit you are taking is the fact that the plaintiff had to sue you in the first place.

Also, even if you can prove that your credit rating has been negatively affected by failure to give you a satisfaction of judgment, how would that translate into money damages?

Have you requested a satisfaction of judgment, in writing?