Stockpile rhymes with:
anglophile, argyle, carlisle, carlyle, carwile, corbeil, costabile, crocodile, erstwhile, exile, francophile, freestyle, gentile, hairstyle, lifestyle, meanwhile, mercantile, oenophile, percentile, peristyle, profile, reconcile, senile, senkbeil, sundial, textile, turnstile, wohlfeil