We found the more stable Swiss meringue to be the best option for this majestic edible tree, since there is a fair amount of piping involved in its construction. Don’t skip the step of letting the meringues dry in the oven — it will finish the drying process without coloring them. If you find your meringues taking on color before they are done baking, make sure your oven temperature is correct and lay a sheet of foil gently over the top of them to avoid more color.
Preheat the oven to 225 ̊ F. Line 2 baking sheets with parchment paper. Trace an 8-inch and a 4-inch circle on 1 sheet of parchment. Trace a 6-inch, 2-inch and 1-inch circle on the second sheet. Flip over both sheets (the circles should still be visible).
Bring a few inches of water to a simmer in a medium saucepan over low heat. Put the egg whites in the bowl of a stand mixer and set the bowl over the saucepan (don’t let the bowl touch the water). Whisk in the granulated sugar and cook, whisking constantly, until the sugar is completely dissolved and the mixture registers 165 ̊ F on an instant-read thermometer, 4 to 5 minutes.
Transfer the bowl to the stand mixer and fit with the whisk attachment; add the cream of tartar. Beat on high speed until glossy with very stiff peaks, 2 to 3 minutes. Add 1 teaspoon vanilla extract and 1/2 teaspoon coconut extract. Reduce the speed to medium and beat until the mixer bowl is no longer hot to the touch, 2 to 3 more minutes.
Transfer about half of the meringue to a pastry bag fitted with a large star tip. Starting with the largest traced circle, pipe a ruffled edge around the perimeter. Use some of the remaining meringue from the bowl to fill the circle so the middle is just slightly higher than the piped border. Pipe a second smaller circle of ruffles on top to create a tiered effect. Repeat with the 6-, 4- and 2-inch circles, creating 2 tiers of ruffles on each. Pipe the 1-inch circle, finishing with a peak on top. Transfer the baking sheets to the oven and bake until the meringues are crisp but not browned, about 2 hours. Turn off the oven and let the meringues cool in the oven.
When ready to assemble, beat the heavy cream in a large bowl with a mixer on medium speed until foamy. Add the cream of coconut and confectioners' sugar, then beat on medium-high speed until soft peaks form, 30 seconds to 1 minute. Add the remaining 1 teaspoon vanilla extract and 1/2 teaspoon coconut extract and whisk just to combine.
Dust all 5 meringue tiers lightly with confectioners' sugar. Set the 8-inch layer on a serving platter or cake stand and spread a thick layer of whipped cream on top, just to where the ruffles start. Repeat with the remaining meringue layers and whipped cream, working from the largest to the smallest meringues to build the tree. Dust with more confectioners' sugar.
Make the tiers ahead but assemble the tree close to serving time so the meringues stay crisp.