Preheat an oven to 350°F.
Oil a 9 X 9-inch baking pan.
Place the cherries, strawberries, peaches or nectarines in a bowl and toss gently together.
Sift the flour, baking powder, baking soda and salt together in a bowl and reserve.
In an electric mixer, cream the butter until light and creamy, 2 minutes. Add the sugar and continue mixing until light and fluffy, 2 minutes. In a separate bowl, whisk together the eggs, rum and lime zest. Gradually add this mixture to the creamed butter and sugar mixture. Add the dry ingredients in 3 batches, mixing after each addition. Add the yogurt and stir just until mixed.
Pour half of the batter into the prepared pan. Spread the fruit evenly over the top. Pour the remaining batter onto the fruit. Bake until a toothpick inserted into the center comes out clean, 30 minutes.
Meanwhile, whip the cream and confectioners' sugar in a bowl until soft peaks form.
Remove the cake from the oven and cool it in the pan. Cut into squares and serve warm or room temperature, with the whipped cream alongside.