Make the teriyaki sauce by first whisking together cornstarch and pineapple juice in a small bowl. Set aside.
In a small sauce pan, whisk together granulated sugar, soy sauce, cider vinegar, garlic, ginger, and black pepper in a small sauce pan over the stove top. Turn heat to medium-high and allow mixture to come to a full boil, while whisking it occasionally so it doesn't burn. After it boils, quickly pour in cornstarch and pineapple juice mixture, while whisking and allow it to return to a boil just until it thickens. Quickly remove it from the heat. Stir and transfer to a sealable container and place in the refrigerator to cool and further thicken.
Place chicken tenderloins and pineapple rings in separate GladĀ® Food Storage Bags. Reserve 1/4 c. teriyaki sauce and pour 1/2 of the remaining sauce into the chicken tenderloin bag and the other 1/2 in the bag with the pineapple rings. Allow these to marinate in the refrigerator for at least 8 hours.
Grill chicken and pineapple rings on medium-high heat, turning once, until chicken is no longer pink inside. At the very end of the grilling process, baste chicken and pineapple with remaining 1/4 c. of teriyaki sauce.
Cut tenderloins, as necessary, to fit on slider rolls. Place chicken and a pineapple slice on a toasted slider roll and serve.