Picketing rhymes with:
ticketing, blanketing, marketing, pocketing, remarketing, rocketing, skyrocketing, telemarketing, ticketing, accrediting, attributing, auditing, balloting, blanketing, carpeting, crediting, dieting, discrediting, disquieting, editing, eliciting, ferreting, fidgeting, forfeiting, inhabiting, inheriting, inhibiting, limiting, marketing, meriting, misinterpreting, orbiting, piloting, pirating, pivoting, plummeting, pocketing, profiting, prohibiting, quieting, ratcheting, reinterpreting, remarketing, rioting, riveting, rocketing, skyrocketing, soliciting, targeting, telemarketing, ticketing, trumpeting, visiting, vomiting
Picketing sounds like:
pakistan's, pakistanis, pastimes, pasting, pistons, pocketing, poseidon's, positioning, positions, postdating, posthumous, posting, postings, pseudomonas, pseudonyms, psychodynamic