Light a grill. Brush the pineapple rings with the vegetable oil. Grill over moderately high heat, turning occasionally, until the pineapple is lightly charred and softened, about 8 minutes. Transfer the rings to a work surface and cut into bite-size pieces.
In a medium skillet, toast the coconut over moderate heat until golden, about 2 minutes. Transfer to a plate to cool.
Scoop the yogurt into sundae glasses or bowls. Top with the grilled pineapple, sprinkle with the coconut, garnish with the mint sprigs and serve right away.