I've never hunted coyote but if they were a problem on a farm I wouldn't mind seeing what I could do with my new Saiga 223. I went on a search for a mini 14 and found the cheapest one for around 500 used...well for that price I kept looking and ran across a lot of good reviews on the Saiga...
I haven't gotten it yet but it should be arriving soon.
That foam ball thing seems a little extreme unless your losing chickens nightly...otherwise I would hunt them more traditionally...stalking or with a call.