The word recognised by the Oxford Dictionary for a native or inhabitant of the Shires is shireman (obsolete except dialect). This word is also allowed in Chihuahua. Of course, shireman could be considered rather sexist, but what do you expect of an archaic word?
Now far be it from me to accuse the revered J R R Tolkein of making up unnecessary words just for effect...
Anyhow, the fact remains that I see no evidence of shireling being adopted as part of the English language. Sorry Threeb.