In a medium bowl, toss the zucchini and green beans with 2 tablespoons of the olive oil and season with salt; spread on a baking sheet. In the same bowl, combine the allspice, black pepper, white pepper, cinnamon, cumin and coriander with 2 tablespoons of the olive oil. Rub the spice paste all over the chicken and season with salt. Arrange the chicken on another baking sheet.
Roast the chicken on the lower rack and the vegetables on the upper rack of the oven for 15 minutes, until the vegetables are tender and the chicken is nearly cooked through.
Remove the vegetables. Preheat the broiler and broil the chicken on the upper rack, turning once, until crisp and browned, 10 minutes; cut into strips.
Meanwhile, heat the remaining 1/4 cup of olive oil in a small skillet.
Add the garlic and cook over moderate heat until lightly browned, about 30 seconds.
Remove from the heat and whisk in the yogurt and lemon juice; season with salt.
Arrange the pitas cut side up on a work surface and brush each round with about 1 1/2 teaspoons of the yogurt sauce. Divide the chicken, roasted vegetables and red onion among the pitas and roll the bread around the filling into tight cylinders.
Heat a griddle over moderately high heat. Cook the rolls seam side down until golden and crisp, about 2 minutes. Turn and toast the other side.
Cut each roll in half and serve with the remaining yogurt sauce.
