Place the chopped apricots in a small bowl with enough cool water to cover. Let stand 30 minutes, then drain and pat dry with paper towels.
Stir together the peanut butter, honey, and brown sugar in a medium-size heavy-duty saucepan. Cook over medium heat, stirring constantly, just until mixture begins to bubble around the edges and sugar is completely melted, 2 to 3 minutes. Remove from heat. Add the oats, coconut, salt, and chopped apricots; stir well to fully incorporate. Cool 10 minutes.
Dampen hands, and shape mixture into about 24 (1½-inch) balls. Place cookies on parchment paper-lined baking sheets and chill 1 hour. To store, refrigerate in an airtight container for up to 1 week.