If you want predictability and perfect doneness in your meat, I strongly recommend reverse searing your meat. If you can cook on a grill and have a meat thermometer, you've joined the club, you can cook this!
Using a sharp knife score (aka slice) the skin partway (not all the way through) without cutting into the duck meat. Keep scores about ¼” to ½” wide. Turn the duck 180 degrees and score the skin again for a crosshatch pattern.
Season the meat and skin of the breast liberally with your favorite spice rub. I like a sweet rub with a little kick.
Place duck breasts meat down, skin up on smoker and cook for ~10 minutes until internal temperature is 120F (I like my duck at medium rare at 130F) or 10F degrees below your desired finishing temperature. In the meantime, warm up a skillet or grate on hot coals for searing.
When your duck meat is 10F degrees below your desired finishing temperature, sear duck breasts with skin up and meat down for color on skillet or hot grate.
Then, flip duck to sear duck breasts skin down on hot skillet or hot grate until skin is crispy and rendered. Duck should finish 130F for medium rare or 140F for medium or 155F for well done.
Brush on your favorite sweet barbecue sauce on the top of the duck skin.
Rest for at least 10 minutes and lightly cover with a tented foil or lid on a plate.
Slice duck breasts crosswise, against the grain.
SmellaQue Tip: Scoring the skin of duck breasts enables the fat to render without overcooking the duck meat, while becoming a vessel to hold flavor.