Heat oven to 350 degrees.
In an electric mixer, combine cream cheese, sugar, coconut and eggs; set aside. In a small bowl, combine macadamia nuts, graham crackers and butter.
Place six (4-inch diameter) cake rings on a sheet pan and divide the graham cracker mixture evenly between them to form a crust. Divide the cream cheese mixture evenly between the rings. Bake 30 minutes or until cakes are set. Let cakes cool to room temperature before serving. Can be made in advance and stored in refrigerator.
Peel and cut pineapple into 1/2-inch slices and core. Dip pineapple slics in rum and brown sugar. Grill over indirect medium heat until well-marked, 6-8 minutes, turning once halfway through grilling time. Set aside and let cool to room temperature before serving.
Prepare coulis at the last minute by pureeing strawberries and lychees together. To serve, place a pineapple ring on a serving plate and top with a cheesecake. Drizzle with strawberry-lychee coulis.