Counterbid rhymes with:
forbid, bid, forbid, rebid, adid, amid, bid, cid, cyd, did, forbid, grid, hid, id, ihde, kid, kidd, kidde, kyd, lid, madrid, majid, mid, quid, rebid, redid, rid, schmid, sid, skid, slid, smid, squid, stidd, syd, tidd, undid
Counterbid sounds like:
contribute, contributed, contrived, counterfeit, counterfeited