For pie crust. Heat oven to 350 degrees F. In a medium mixing bowl,toss together coconut, sugar, and lime zest. Add butter and stir until crumbly. Press mixture into bottom and up the sides of a 9 inch non stick springform pan. Bake for 10 to 12 minutes, until light brown. Allow to cool completely.
For Filling. Reduce oven temp to 300 degrees F. In a large mixing bowl, with an electric mixer, on medium speed. beat cream cheese until smooth. Gradually beat in sweetened condensed milk, beating until smooth
Add eggs, lime juice, vanilla extract, and cornstarch, mixing until well combined. Pour cream cheese mixture into the prepared crust. Stir in jam until smooth. Drop dollops of jam on top of filling. Gently swirl jam with a knife until top of filling appears marbleized.
Bake for 55 to 60 minutes or until center is set when jiggled. Place pan on a wire rack to cool completely. Cover and refrigerate 8 hours, or overnight.