Unfortunately, some ex's are only too happy to let you carry all the financial weight, even though they are perfectly able to hold a job. After all, why should they work if they can get the court to force you to support them? Not only does this raise your child support to the maximum amount (because the other parent "has no income"), it also sets an extremely poor example for the child. BOTH parents have a duty and an obligation to support their children, whether or not they are divorced.
If your ex is able to work but refuses to do so, find out if you can request a vocational evaluation. What this will do is send your ex to one or more occupational therapists or counselors to determine what marketable job skills they have, if he or she needs any training, and most importantly, how long it will take for them to be fully and gainfully employed again. This sets up a time limit of sorts that will force the issue of when he or she will have to go back to work and help provide for the child. This is what you want to stress- that they have the ability to work, and should do so. You're not asking for anything outrageous- you simply want them to help support the child.
The cost of a vocational evaluation will range from $500 to $1000, possibly more in some cases. Not all States recognize this, so check around and find out if this is an option for you. If it is, give it some serious consideration- even if your child support is reduced by only $100, in the long run the money you save will be worth the cost of the vocational evaluation. The younger the child, the more you will save across the time in which you pay support. See if you can get your ex to pay for some of the costs associated with the vocational evaluation, whether by agreement or court order. Some programs allow for repayment of the vocational evaluation fees once the person becomes employed, so check into that as well.
Find out what their previous occupation was and use that as a starting point to show the court that your ex is capable of holding a job and earning a living. Also find out if he or she has any disabilities that would exclude them from certain jobs (i.e. back problems, carpal tunnel syndrome, etc). If they do have legitimate disabilities, generate a list of various jobs that they can perform. In short, show the court that they are capable of employment in order to assist in the support of the child.
Once they're employed, request a commensurate reduction in your support amount. This is entirely reasonable- if your support amount was based on you being the sole wage-earner, it is only fair that the amount be reduced since they are now employed and receiving an income.