Eggcups rhymes with:
linkups, backups, buttercups, checkups, hookups, linkups, markups, pickups, shakeups, backups, buildups, buttercups, checkups, cleanups, coverups, grownups, hangups, holdups, hookups, lineups, linkups, markups, pickups, push-ups, pushups, runups, setups, shakeups, startups
Eggcups sounds like:
ejup's, ekofisk, equifax, equips, escapees, escapes, eschbach, eshbach, eshbaugh, esophagus, espejo, espouse, espouses, espy's, expos, expose, exposes