Especially since the '08 financial crash, many people have lost their job. However, don't assume your child support order will automatically go down.
1 - File a Modification Petition
In NY, one only gets reflief retroactive to the date of filing, so if you lose your job, file a petition for modification right away. You cannot get a modification if you either voluntarily quit or are fired due to misconduct.
2 - Burden of Proof
On your petition, you have the burden of proving you lost your job thru no fault of your own. Thus, you must produce a notarized letter from your ex-employer confirming you were laid off, or other similar proof. You must ALSO prove you're making a diligent job search. You can generally only prove this by submitting a job search diary, comprising printouts & recordations of all your efforts to find work commensurate with your prior earnings. You should be aware that if you're completely out-of-work, the Court will generally require 30-40+ efforts per week. If you're working part-time, this may be reduced depending on your hours to 10-30 efforts per week.