We examine how to synthesize a parallel schedule of structured traversals over trees. In our system, programs are declaratively specified as attribute grammars. Our synthesizer automatically, correctly, and quickly schedules the attribute grammar as a composition of parallel tree traversals. Our downstream compiler optimizes for GPUs and multicore CPUs. We provide support for designing efficient schedules. First, we introduce a declarative language of schedules where programmers may constrain any part of the schedule and the synthesizer will complete and autotune the rest. Furthermore, the synthesizer answers debugging queries about how schedules may be completed. We evaluate our approach with two case studies. First, we created the first parallel schedule for a large fragment of CSS and report a 3X multicore speedup. Second, we created an interactive GPU-accelerated animation of over 100,000 nodes.