Choose a pineapple that's plump, with a firm body and fresh, green leaves. If you aren't going to use it right away, store it whole in the fridge.
Preheat oven to 350°F. Mist 2 baking sheets with cooking spray.
Combine sugar, cinnamon, allspice and nutmeg in a small bowl. Lightly mist both sides of a tortilla with cooking spray and sprinkle with sugar mixture. Repeat with remaining tortillas, stacking them. With a sharp knife, cut tortilla stack in half, then cut each half into thirds, making 24 wedges total. Place wedges in a single layer on baking sheets. Bake until chips are crisp and golden brown, 10 to 12 minutes, rotating pans halfway through. Let cool on a wire rack.
Toss coconut, fruit and juice in a bowl. Spoon salsa into dessert cups and serve with cooled chips.