For pineapple syrup, combine pineapple, sugar, lime juice and ½ cup water in a saucepan and stir over medium-high heat until sugar dissolves. Bring to the boil and simmer for 15 minutes or until syrupy. Cool, add rum and strain, discarding solids. Cool completely.
Preheat oven to 160C. Beat butter and sugar using an electric mixer until pale and fluffy, add egg and buttermilk and beat to combine. Stir in flour, coconut and pineapple, then spoon mixture into 10 greased and floured 1/3 cup-capacity brioche or dariole moulds and bake for 20 minutes or until golden and a skewer withdraws clean.
Turn cakes from moulds, pour over half the syrup and cool on a wire rack. Serve with remaining syrup and sliced pineapple.