Cut four ¼ inch thick rounds from pineapple; set aside. Cut remaining pineapple into large chunks. In a food processor, combine pineapple chunks, scallions, chile, thyme, garlic, allspice, and olive oil and pulse until almost smooth.
Place tofu and reserved pineapple slices in shallow dish. Cover with pineapple marinade, turn to coat. Cover with plastic wrap and refrigerate 1–2 hours. (Don't refrigerate longer than that or the pineapple juice will make the tofu mushy.)
Heat grill to medium-high and brush or spray with olive oil. Brush excess marinade from tofu and pineapple and place on grill. Cook approximately 8 minutes (or until lightly browned), turn, and cook the other side for approximately 8 minutes more. Serve with leftover marinade.