For Pie Crust: HEAT oven to 350°F. Toss together coconut, sugar and lime zest in a medium mixing bowl. Add butter and stir until crumbly. Press mixture into bottom and up sides of a 9-inch non-stick spring form pan. Bake for 10 to 12 minutes, until light brown. Allow to cool completely.
For Filling: REDUCE oven temperature to 300°F. Beat cream cheese until smooth with an electric mixer on medium speed in a large mixing bowl. 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 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 wire rack to cool completely. Cover and refrigerate 8 hours to overnight.