Place the chicken breasts in the bottom of the pressure cooker insert in a single layer.
In a mixing bowl, whisk together the chicken stock, pineapple juice, ketchup, soy sauce, rice vinegar, honey, and pepper until well combined.
Pour the sauce mixture evenly over the chicken in the pressure cooker.
Secure the lid, set the pressure to high, and cook for 10 minutes.
When cooking finishes, allow a natural pressure release for 10 minutes, then carefully quick-release any remaining steam and remove the chicken to rest.
Turn the cooker to Sauté. Add the chopped green pepper and onion and bring the liquid to a boil while shredding or chopping the rested chicken.
Whisk the cornstarch with the cold water to make a slurry, then stir it into the hot sauce in the cooker.
Cook, stirring, until the sauce thickens, about 1–2 minutes, then add the shredded chicken back and stir to coat and heat through. Turn off the cooker.
Serve the sweet and sour chicken hot over rice.