To make the brine, combine the salt, sugar, water, lemon, peppercorns, mustard seeds, and coriander seeds in a medium saucepan and heat over medium heat, whisking occasionally, until the salt and sugar dissolve, about 5 minutes. Transfer to a medium-large bowl, add the coffee, and refrigerate until cool, about 15 minutes. Put the chicken breasts in the brine and set a pot lid or small plate on top to keep them submerged. Refrigerate them in the brine for 2 to 3 hours.
Heat a gas grill to high or prepare a hot charcoal fire. If using wood chips with a gas grill, pile them in the smoker box or in a smoker pouch (see How to Add Smoke to a Gas Grill). Run your grill on high until you see smoke. If using a charcoal grill, toss the wood chips directly onto the hot coals.
Drain the chicken and blot dry with paper towels. Lightly brush both sides with the melted butter or oil. Arrange the breasts on the grill at a 45-degree angle to the bars of the grate. Grill until they have grill marks, about 2 minutes, and then rotate them 90 degrees (to get a crosshatch of grill marks) and continue grilling for 2 to 4 minutes. Flip the breasts and cook unitl they're firm to the touch, another 4 to 6 minutes. Serve immediately.