It means irritable, touchy, bad-tempered, always finding fault. It came from Scotland where it is also found as curnaptious. Car is an intensifying prefix and nap is from knap in the sense to bite, to snap, related to Dutch or Low German knappen, to break with a sharp crack. The ending -tious is used as in loan words from Latin.
The word is listed in Macafee's Concise Ulster Dictionary. I've heard it in antrim, Down, Fermanagh and Donegal. The Dictionary of the Scots Language has the word without the car prefix from some of the northern counties of England close to the Scottish border. 'He's a (k)naptious little man.' Oxford has four citations, two of them from Ulster. This is one, from W G Lyttle's Readings by Robin (1878): 'He's a cross carnapshus wee brat, so he is!' A good word it is, no matter how you spell it.