Heres a recipe I use and there Awesome, I would just throw some Alder on the coals while there cooking. Not sure if this is what your looking for
Grilled Oysters
32 oysters, on the half shell
1 cup (2 sticks) butter
2 tablespoons finely chopped garlic
1/2 teaspoon freshly ground black pepper
1/4 cup grated Parmesan cheese (use Parmagiano Reggiano)
1/4 cup grated pecorino Romano cheese
1/2 cup finely chopped parsley
Have a bunch of fresh french bread handy for sopping up juices!
Heat the grill over medium-high heat.
Melt the butter with the garlic and pepper in a large skillet. Mix the Parmagiano and Romano cheeses in a small bowl.
Spoon some of the melted butter mixture onto each oyster. Add a pinch of the combined cheeses to each oyster, add a pinch of parsley, then place on the grill. Grill the oysters until they are hot,bubbly and puffed, about 8 minutes.
Grilled oysters on the half shell with Garlic spears.