Try looking up the ordinances for towns near you to see how they've handled it as well.
I just found this page, might be helpful: https://www.backyardchickens.com/articles/chicken-laws-and-ordinances-and-how-to-change-them.65675/
I would think any kind of local forum would be a good place to start. Maybe even a farm supply store or something similar would let you put up a flier? I grew up in a town of 600 so I probably would have put a flier at the gas station or thrift store. Lots of farm families around my town would...
I would try to find other like-minded people in your area and have them attend the next city council meeting with you. Do you have a local Facebook page for chickens or homesteading? Maybe one of them has experience with this kind of local activism. If you can arrange a meeting with a city...