Auctioning rhymes with:
functioning, malfunctioning, sanctioning, sectioning, airconditioning, apportioning, auditioning, captioning, cautioning, commissioning, conditioning, cushioning, decommissioning, fashioning, freshening, functioning, malfunctioning, mentioning, motioning, optioning, partitioning, petitioning, positioning, rationing, reconditioning, repositioning, sanctioning, sectioning, stationing, transitioning, vacationing
Auctioning sounds like:
academic, academics, academies, academy's, acceding, accosting, accusations, acquisition's, acquisitions, acquitting, acting, actinomycosis, action's, actions, acuteness, agitating, ashton's, assistance, assisting, associating, association's, associations, astonish, astuteness, auction's, auctions, augustinians, augustyniak, austen's, austin's