Here's what rhymes with priggishness.
piggishness Words that almost rhyme with priggishness
impishness willingness cliquishness skittishness griminess fierceness siliceous implicitness filminess precipitous litigants spirituous explicitness spiritless duplicitous jinrickshas jinrikshas ubiquitous iniquitous indigents coincidence certificates significance serendipitous insignificance