Packer rhymes with:
acker, aker, akre, attacker, backer, bakker, blacker, bracher, bracker, cracker, hacker, lacher, lacquer, macher, makar, racker, sacher, schacher, slacker, stacker, tacker, thacher, thacker, thakkar, tracker, vanacker, wacker, whacker, zacher
Packer sounds like:
paccar, pacer, packager, pagar, pager, passaro, passer, passero, paxar, peacher, pechora, pecor, pecora, pecoraro, pecore, peguero, peiser, pekar, peshawar, peyser, pfizer, picaro, picher, pickar, picker, pickier, picower, piker, pixar, pizarro, pizer, pizzazier, pizzeria, poacher, poker, pooser, poser, possessor, poucher, poyser, pucker, pusher, puskar, pysher