Aligning rhymes with:
realigning, declining, lining, realigning, reclining, affining, assigning, breining, brining, combining, confining, declining, defining, designing, dining, divining, fining, lining, mining, opining, pining, realigning, reassigning, reclining, redefining, redesigning, refining, resigning, shining, signing, twining, vanhyning, vining, whining, wining
Aligning sounds like:
alaskans, alcan's, aligns, alkanes, alkenes, alleghenies, allegheny's, allegiance, allegiances, alleging, allgemeines, allison's, allusions