You build your case. Dozens of photos or videos of clean coops. Get testimonials from neighbors of other chicken owners about the lack of smell, etc. Be kind but resolute. Do not fold at the first setback. Don't get angry or demanding. Show your plan of how you will raise your chickens in a way that speaks to all the objections the city has. Get two or more veteran chicken owners from other cities to endorse your plan. Get written statements from other cities that decided to change their laws to favor backyard flocks and why.
Also, there is a section here on BYC devoted to changing local laws. Might be worth checking out if you haven't already.
Also, there is a section here on BYC devoted to changing local laws. Might be worth checking out if you haven't already.