Preheat oven to 375°F.
Spread 3/4 cup coconut evenly on a baking sheet and toast in middle of oven, stirring once, until golden, about 8 minutes, then cool.
Blend together flour, sugars, and salt in a food processor, then add butter and blend until a dough begins to form. Transfer to a bowl and knead in oats and toasted coconut until combined well.
Reserve 3/4 cup dough, then press remainder evenly into bottom of a buttered 13- by 9-inch metal baking pan and spread jam over it.
Crumble reserved dough evenly over jam, then sprinkle with remaining 3/4 cup (untoasted) coconut.
Bake in middle of oven until golden, 20 to 25 minutes, then cool completely in pan on a rack.
Loosen from sides of pan with a sharp knife, then lift out in 1 piece and transfer to a cutting board.
Cut into 24 bars.
Bars can be made 3 days ahead and kept in an airtight container at room temperature.