Preheat a grill to medium and oil the grates.
Slice the potatoes about 3/4 inch thick. Place them in a bowl and add the canola oil, paprika, 2 teaspoons salt, and 2 teaspoons pepper. Toss to coat.
Place the potatoes on the grill, cut-side down and grill until lightly golden brown.
Turn the potatoes over and continue grilling until just cooked through.
Remove and allow to cool completely. Dice into 3/4-to-1-inch pieces.
In a large glass bowl, combine the diced potatoes, celery, red onion, and cilantro.
In a medium glass bowl, combine the sour cream, mayonnaise, mustard, capers, juice, 1 teaspoon salt, and 2 teaspoons pepper.
Fold the mayonnaise mixture into the potato mixture until thoroughly coated.
Cover and refrigerate for 20 to 30 minutes.
Stir and adjust the seasoning as needed.