Generally, employers with 15 or more employees are required to provide employees who have disabilities with a "reasonable accommodation." A reasonable accommodation is a small (or sometimes large) change to your work environment which will enable you to perform your job. Reasonable accommodations can come in the form of providing employees with physical items such as special chairs, non-physical items such as flexible schedules, etc. Your employer does not have to provide you with the reasonable accommodation that you suggested, but some type of reasonable accommodation. They are able to propose a different reasonable accommodation that may solve the issue you're having but may be better for their business.
Once you request your reasonable accommodation from your employer (or even notify your employer of your disability), the employer is required to enter into an informal "interactive process." If the employer wants to grant your accommodation outright, great! Stop reading. If not, the interactive process is the next step. Your employer does have the right to ask some reasonable questions, require reasonable documentation, and propose an alternative reasonable accommodation than the one you've proposed. This a time when you and your employer should be working with each other to come to a mutually agreed up on solution to the problem.
Lastly, while the employer is required to explore the possibility of a reasonable accommodation, if an accommodation would pose an "undue hardship" to their business, they're not required by law to adopt it. This is frequently the case in smaller employers. Sometimes employers with less resources and staff face unreasonable burdens trying to accommodate even 'reasonable' accommodations.
Additional resources provided by the author
For more information on this issue, contact an employment attorney in your area. Also, there are many great resources online that can answer many questions. The Equal Employment Opportunity Commission's (EEOC) website has helpful sections of FAQs and guidelines that cover many questions. If you have any questions, please feel free to contact me.