Oh, don’t mention shooting them, the PETA people will have fits. Try putting a few rat traps on top of fence posts. Drill hole and tie them to post with couple feet of slack. No bait needed.
In Louisiana crows are considered "Pest" and may be taken from Sept. 1 through Jan. 1 , with no limit ...
If crows are depredating or about to depredate ... any crops , ornamental plants , shade trees , agricultural trees or plants , livestock . wildlife , or when concentrated in such numbers as to be a nusiance and/ or the spread of West Nile Virus ... may be taken year round , no limit .
Gary
I live in a rural area but have neighbors close by. I don't use a shotgun anymore as the neighbors are more sensitive to gunfire than they used to be. All of them are newish from the pavement except one. I use a scoped model 36 RWS now. It kills crows about like a 22 short would (900 fps) but range is +/- 50 yards. Good from cover if you call them in. They know when you drop one and mark the area as hazardous to their health.
I know, buying a $400 air rifle isn't a solution for most but I've had mine since I lived in town which was about 27 years ago. I used to shoot rats and starlings with it in town and nobody knew. Silent and deadly.