The first thing you need to know is whether or not the creditor has sold the judgment to a debt collector. Most debt collectors pay 5-10% of the judgment value, and sometimes less. So, your ability to negotiate increases substantially once the debt is sold.
If your credit report shows a debt collection account, then that would immediately tell you that the note is sold. Otherwise, you can contact the original judgment creditor and simply ask if they will consider a settlement, and if they say yes, then that means they still own the note. You can also check the court file where the judgment was entered, because in order to assign the judgment, the assignment must be filed with the court. This is the most reliable method.
Once you know who owns the judgment debt, you can send a letter and make an offer. Pick a number above the 10% that the debt collector would pay, because that's more than either is likely to get. Then mention something about the fact that if you cannot negotiate a settlement that you will be forced to file Chapter 7
Even if this is not true, the creditor will know that unless it negotiates, there is a chance that it will be discharged entirely from the judgment and get nothing at all, if you file bankruptcy. The creditor also knows that a typical Chapter 7bankruptcy runs about $2,500 if you hire an attorney, so you could mention that you know how to do the paperwork, so that it will cost you no more than a few hundred dollars in filing fees.
The point is that you want to provide a picture that the creditor doesn't have a snowball's chance of ever collecting more than you're offering.
Then see if you get a response. If you do, come on back and we can talk about the process of making sure that you don't pay the judgment and then have the creditor refuse to remove the credit ding, because that is a completely separate and somewhat more complex issue.
Hope this helps.