In a saucepan off the heat, combine the sugar and cornstarch with a whisk. Add the coconut milk and water. Bring to a boil while stirring and simmer gently for about 10 seconds. Remove from the heat. Add the lime juice. Pour into a Popsicle mould. Insert the sticks. Freeze for 5 to 6 hours.
In a food processor, purée the mango and sugar until smooth. If necessary, add water.
Unmould the popsicles and dip in the mango coulis. Serve immediately.