In a small saucepan combine the butter, brown sugar, lime peel, and lime juice. Whisk over medium heat until butter is melted and sugar is dissolved.
Quarter the pineapple lengthwise. Cut the core from each piece and discard core. Cut each quarter in half crosswise to create 8 rectangular pieces.
Heat the grill to medium and brush the grates with canola oil. Add the pineapple to the grill rack; grill for 3 minutes. Brush with lime mixture; turn. Brush again with lime mixture. Grill for 3 minutes more, brushing occasionally with remaining lime mixture (watch for flare-ups). Remove to a cutting board and slice each pineapple piece in half. Serve each person 2 pieces of pineapple with a scoop of yogurt.