Pickren rhymes with:
askren, corcoran, saccharin, aldebaran, amparan, anaren, andren, askren, bargeron, bundren, cameron, catherine, coldren, condren, corcoran, cothren, fondren, halloran, hefferan, hefferon, hendren, holdren, holleran, holloran, killoran, lutheran, mandarin, margarine, milliron, motoren, nitroglycerin, nitroglycerine, o'hallaron, o'halloran, o'halloron, ohalloran, operan, orgeron, saccharin, saharan, tamarin, tiberon, uterine, veteran, voltaren
Pickren sounds like:
pagurian, pegram, pickron, pogrom, pokorney, pokorny, popcorn