When a credit has a court judgment, they have the power and you have very little protection from them. Unless you file bankruptcy, your only protection is contained in state laws called exemptions & I am posting a link to a description of these exemptions below.
Many times creditors do agree to accept payments from debtors instead of garnishing, but the creditor is unlike to accept payments significantly smaller than what they would receive from a wage garnishment. So if you send them $200, and you are making more than $800 per month, from their perspective, they are taking a lot less than they would be an order garnishing you. No wonder you haven't been able to persuade them to let you make these payments. Hope this perspective helps!
Because you are currently being sued, and there is not yet a judgment against you, they cannot yet garnish your wages. A private party, meaning not the government, must first sue you, obtain a judgment against you, and then must obtain a court order to garnish your wages. Wage garnishment applies to W2 employees. If you are not a W2 employee, the creditor may seek a court order to levy your bank account for the amount of the judgment.
Generally if a creditor obtains a judgment against you and a court order to garnish your wages, then you have to make them an offer more attractive than garnishing your wages. This is usually a lump sum payment for less than the judgment amount. Garnished wages are often held in escrow until the full amount has accumulated. This means the creditor may be interested in settling for a lesser amount they can collect faster.
Before judgment, consult an attorney and try to settle this matter. Settlement options including term payments are more likely before judgment. Settlement before judgment may be more attractive to your creditor because of the costs involved with litigation and garnishing your wages.
Each State has different garnishment laws. Often times the laws with respect to garnishment may be the laws from the State that the judgment was had and/or the person is paid. The question needs to be more specific as to the type of garnishment and what it to be garnished to properly answer it. Of course if you are dealing with a creditor in this case the medical provided and they agree to a payment plan to avoid garnishment then of course. But these folks seem hell bent on all the money up front and I am not familiar with Ok laws or enough facts to supply an answer other than as per the above.