Pour enough oil into a deep fryer or large heavy pot to reach 3 to 4 inches deep and heat to 350°F (175°C), monitoring with a thermometer.
In one bowl, whisk together 2 cups all-purpose flour, 2 teaspoons salt, and 2 teaspoons ground black pepper.
In a second bowl, combine 1 cup buttermilk and 1/2 cup water and whisk until blended.
Pat the chicken tenders dry with paper towels and lightly season both sides with a pinch of salt and pepper.
Working with one piece at a time, dredge each tender in the seasoned flour, then dip into the buttermilk mixture, then dredge again in the flour to coat thoroughly.
Carefully lower the coated tenders into the hot oil and fry, turning once, until golden brown and cooked through, about 7 to 8 minutes total per batch.
Remove the tenders with tongs and drain on a wire rack set over a rimmed baking sheet before serving.