Those cities' ordinances are a good resource if you plan on making a pitch to your city council. I'd look at what their restrictions are and maybe try to make a proposal that falls in line with what the surrounding cities have. A reasonable request is more likely to get heard and considered.
^^^ this.
One of the best ways to change an Ordinance is to point at the neighbors and say, "Hey? Why are we the oddity???" It also helps that you are on the border, so to speak - even if you can't get an Ordinance change, possibly you could get a zoning change. I've not looked up your County, or your Municipality, to inspect the zoning closely, but...
Its common in many places that aren't too built up to have a "buffer" zone, not very wide, comprised of lots which are zoned "RA" "Rural Agricultural" or "RR" "Rural Residential" or something similar, which blend the characteristics of both zones.
You might also point out, in your efforts, the fragility in food distribution revealed by the recent pandemic, the resurgence of popularity in home poultry ownership, the economic benefits of cottage industries after the massive business closures we've seen this past year, and even the environmental benefits of a well managed flock - then be prepared to assist in the drafting of model zoning to address concern with noise and odor, if (when) they arise.
Opposing you will be those who have witnessed the meteoric rise in home valuations on their own properties in the surrounding area who worry, rightly or wrongly, that a nearby chicken coop would negatively impact their home value. A concern they might reconsider when they see their new tax assessment...
