You will need to contact the court and let them know of your hardship. This will keep you out of jail for the delinquency. Then, you need to make arrangements to pay because the longer that you do not pay, the more that you owe and things like tax returns, unemployment payments and government loans will be attached.
Your first priority is to call the child support agency for your county and let them know the situation. Most agencies will work out something as long as you keep them informed. Usually the late payments will accrue and you'll have to pay it eventually. The next step is finding a job. Remember that your children are depending on you.
You can request a reduction in payment amount due to hardship. You can request family members to pay the bill for you as a personal loan to avoid jail or losing your license.
You have to petition the court that you are attempting to find work but currently do not have a job or other assets to sell to pay the support. You have to convince the judge you are attempting to make a good faith effort to find work and provide the support.