Preheat the oven to 375ºF. Drain and rinse the black beans. Place the black beans in a large bowl and mash them slightly with your hands or a potato masher. Slice the green onions and add them to the bowl along with the chili powder, cumin, garlic powder, cayenne pepper, and salt. Stir until the beans are evenly seasoned.
Add the ground turkey to the seasoned black beans. Mix well using your hands. Form 10 small patties (about 2-2.5 inches diameter, 1/2 inch thick). Place the patties on a roasting pan or a baking sheet covered with foil and wire cooling racks.
Bake the patties in the preheated oven for 20 minutes, or until browned on the outside and no longer pink in the center. Alternatively, you can cook the patties in a skillet, on a grill, or using an indoor countertop grill.
While the patties are baking, prepare the avocado sauce. Add the avocado (diced), juice from half a lime (about 2 Tbsp), garlic powder, salt, sugar, sour cream, and 2-4 Tbsp of water to a blender. Blend the ingredients together, adding the water slowly until a smooth, thick sauce forms.
Smear some of the sauce inside each pita half, add a couple tomato slices, and two of the turkey patties.