I've done many ducks over the years - sometimes 2-3 at a time for holiday parties. I inject them with a mixture of port wine (1 cup) and Lagasse's Essance (2 Tsp). Put my regular rub on the outside, an apple and onion on the inside, and let them sit overnight in the fridge.
Put them on the smoker with a mix of hickory and mesquite. I usually cook them till 180 in the brest and thigh. Usually takes 5-5 1/2 hours. When I get it right, the fat has rendered, the skin is crispy, and the meat is falling off the bones. Really fantastic.
Now, having said that, I was doing these long before I came across this site and was pretty mich winging it. I would guess that smoker temps were around 250 or so.
Knowing what I know now, I would probably kick the temps up to 325 or so to help crisp the skin (mine didn't always crisp up - depending on where they were in the Brinkman box - I am pretty sure now that this was due to non-uniform temps in the box). Given the amount of fat that has to render, I would probably try that at the end after most of the fat has rendered. I have also seen Lagasse poke small holes in the skin with a fork to help the fat render when roasting a duck. Might try that.
Hope this helps a little. We really like them. And the left overs make a killer Duck and Anduille sausage gumbo!
Forgot to add that I mop with apple juice, cider vinegar, and some rub.