As it was mentioned, try a electric fence and including music!
IF you have a farm supply store near by, you should be able to get a low cost solution for under $50 and with wire and say plastic/fiberglass poles, you should be able to secure your coop for less than $100.
Run two rows around your coop area, close as possible in most areas so if something runs through the fence, it won't have any room to roam around inside it without making contact again with the electric fence. with the first run of wire about 6-8 inchs from the ground and the second about 12 inchs above that; a third run around would even be better.
On the electric fence charger, solor powered is an option if AC supply isn't available, these run off batteries which charge during the sunlight hours, but you can get non-solor which run off batteries too which require you to replace the batteries
I have not had any critters (yet) get into my coop and I keep a radio on in my garage which is about 50 yards away from the coop, with my history of no critters I'm scared to not turn it off. I have heard of some who use motion light detectors wired up to radios so that it only come on when something triggers it; in this manner the critters won't become use to the noise and it provides a signal to you that something is prowling around be it human or animal.
Trapping/shooting may not be an option since too as already mentioned, others will simply take their place so it better to attempt to keep them loosely trained and condition to stay away.