Simmer water, sugar, and ginger in a small saucepan 5 minutes. Remove from heat; pour liquid through a wire-mesh strainer into a small bowl, discarding ginger. Stir in lime juice; cover and chill syrup.
Combine kiwifruit and next 4 ingredients in a trifle bowl or large serving bowl. Drizzle cooled syrup over fruit; toss gently. Sprinkle with toasted coconut.