Combine rhubarb, sugar and water in a saucepan over medium-high heat. Bring to a boil, then reduce to a simmer and cover. Allow to simmer for about 15-20 minutes, stirring occasionally.
Remove from heat, and strain thoroughly. The easiest way to get all the rhubarb flavor is to use a spoon and press the juices from the pulp in a mesh strainer. Allow to cool. Store rhubarb simple syrup for future cocktails in sealed jar in refrigerator for up to 10 days.
For the Basil Syrup: Combine water, sugar, and basil leaves in a saucepan. Bring to a boil, then reduce to a simmer and cover. Allow to simmer for about 15-20 minutes, stirring occasionally.
Remove from heat, and allow to cool. Strain through a mesh strainer. Basil syrup keeps for one week in a sealed glass jar in the refrigerator.
For the Coconut Rhubarb Basil Cocktail:
Combine all ingredients, except ice in a cocktail shaker. Shake and pour over ice. Garnish with Basil and enjoy!