In a large bowl, combine the ground chicken, breadcrumbs, mayonnaise, 2 tablespoons of the teriyaki sauce, cilantro, salt and pepper until just combined. Do not overwork.
Shape into 4 equal sized patties, pressing your thumb into the center of each one to make a divot. Place them on a plate and refrigerate for 30 minutes.
Meanwhile, preheat a grill on medium high heat. Cook the pineapple rings and onions, about 4-5 minutes per side until the onion is tender. Set aside.
Place the burgers on the grill and cook for 4-6 minutes on the first side. Flip, cooking 4-6 minutes longer, until the burgers are fully cooked through (a thermometer should read 165F). Brush the burgers with teriyaki sauce and flip to brush the other side. Flip them once more to caramelize the sauce a little on both sides. Set aside to rest for 5-10 minutes.
While the burgers are resting, lightly grill the buns.
Top each bottom half with a chicken patty, red onion slices and a slice of pineapple. Add the top bun and serve with more teriyaki sauce on the side.