Here is the way we have done it many times,
"Official Cardogs BBQ Salmon"
"Official Cardogs BBQ Salmon" recipe with TVWB, and I've posted it below in its entirety.
Dry Rub
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1 cup light brown sugar, packed
1 cup non-iodized table salt
3 TBSP granulated garlic powder
3 TBSP granulated onion 1 TBSP dried dill weed
1 TBSP dried savory
2 tsp dried tarragon
Mix all ingredients thoroughly. Turbinado sugar may be substituted for brown sugar. To substitute garlic salt and onion salt, reduce table salt to 1/2 cup and double garlic salt and onion salt to 6 TBSP.
Finishing Rub
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1/4 cup light brown sugar, packed
1 TBSP granulated garlic powder
1 TBSP granulated onion 1 tsp dried savory
1 tsp dried tarragon
Mix all ingredients thoroughly. Turbinado sugar may be substituted for brown sugar.
Buy a fresh, 3-pound salmon fillet, preferably Sockeye or King. Remove the pin bones using tweezers or needle nose pliers. Do not remove the skin. Place skin-side down in a glass or stainless steel pan.
Pack the dry rub on the flesh side of the fillet, approximately 1/4" thick. Let the fillet rest in the refrigerator for 2 to 3 hours (the longer you leave the rub on, the stronger the salt flavor). Rinse the fillet in cool, clean water to remove the dry rub, then pat dry. Allow to dry for about 30 minutes, until the flesh becomes tacky.
Heat a barbecue grill to medium to medium-high. Sprinkle finishing rub on the fillet (twice what you would use as if you were heavy salt and peppering). Cook with the lid closed to an internal temp of 140-155°F (your preference) measured in the center of the thickest part of the fillet.
We recommend using wood to produce smoke while cooking. On a charcoal grill, just sprinkle a few wood chips on the coals. On a gas grill, place wood chips in a pouch made of aluminum foil. Poke holes in the top of the pouch and place it on the hottest spot under the grill. Alder is our wood of choice, but fruitwoods are a wonderful substitute.
You can also smoke it at lower temps of 225-250°F; this allows for more smoke on the fillets