James McAllister and Sons are the likely source of your
bottle.
http://www.potstill.de/oldads.htm
includes a pic of one of their ads.
They were apparently
operational from at least the 1850s, but when Alfred Barnard
visited Ireland in the late 1880s he made no mention of them
having a functioning distillery, though they appear to have
continued marketing whiskey well after that date.
My best
guess is that they were bottlers and bonders. There were plenty
such in Ireland at that time, bottling own label whiskeys, and
Mitchells are the last of that honourable tradition in Ireland
today.
I know Irish Whiskey Chaser possesses a bottle of
one brand of theirs called Clan Colla, so perhaps he might be
able to shed more light?