I thought you must be nuts -- pimentos don't grow on trees, they're plucked out of olives ;^), so I googled, and found you were right: everybody mentions pimento wood when talking about authentic jerk, and a little further digging revealed that the Jamaican pimento is what we call the allspice berry, which does indeed grow on trees.
I did find one place that says they "import the actual Pimento wood to make this As close to island form as possible." Try giving them a call, maybe they can ship you a few sticks.
Another place makes bowls out of the root burls, but doesn't currently have any for sale (you probably want green wood for smoking anyway, according to the recipes I gleaned).
A post on epicurious asked the same question, the answer might be too brief to use:
My personal gut feeling is that you could probably get close to true with other wood chunks such as apple, and soak some allspice berries to throw on the fire.
Wanna cook like an islander,you gotta go to the island...GOOSE ISLAND!!
Berger Brothers has charcoal in almost any form you can think of as well as a good assortment of hardwoods for smoking.Pimento might be a long shot though.
Berger Bros.charcoal supply
1176 N Cherry St (at Division)
312 666 8624
Berger is a great recommendation, though I typically go to Berger for hardwood charcoal (lump) and Chicago Firewood, a couple of blocks away for wood.
Chicago Firewood's wood is cut to fireplace size, easy to chunk or split at home. Usually, though not always, they have maple, apple, cherry, pecan and some of the more exotic woods, always oak and hickory. I've never seen pimento wood at CF, and I have asked once or twice.
1300 N Halsted (Rear Lot)
Berger Brother's Charcoal
1176 N Cherry Ave
Chicago, IL 6062
re: G Wiv
Thanks for the rec.on Chicago firewood.Another source for lump charcoal,a little closer to home is the Farmers Garden Market on Lawrence and Oakley.40lb bags run about $15.00.
Never fail question from the older Greek woman who owns the place "watta you cook,da goat?"