No matter how much you earn, or don't earn, there is never a time when it's appropriate not to take care of your child. This also applies to child support.
If you have a child and are not the primary caregiver, you may be ordered to pay child support. Even if your situation is dire, the court still expects you to put your child first. In a two-parent relationship, the same would be true, so the same still applies after a divorce.
Is there any way to avoid paying child support?
The only legal ways are to give up your parental rights through adoption or other legal processes. If your child grows up and is no longer a minor, you may no longer have to pay. Children who become active duty members may not receive support, and emancipated children don't receive support.
What should you do if you can't afford support because you have no job?
Even in the case that you have no job, you'll still have to pay in most circumstances. The state has a minimum payment threshold that you will need to meet. For most people, it's possible to make this payment thanks to unemployment benefits or through other sources of income that they have temporarily. If you don't pay, the state can garnish your wages, take your tax return for back payments or even arrest you and place you in jail in some instances.
The best course of action is to make payments on time. If you can't afford them, a modification of child support could help.