Avoidance rhymes with:
abundance, accordance, ascendance, attendance, cadence, coincidence, confidence, correspondence, credence, decadence, dependence, evidence, guidance, impedance, imprudence, incidence, independence, interdependence, jurisprudence, kloberdanz, overabundance, overconfidence, overdependence, precedence, providence, prudence, residence, riddance, self-confidence, subsidence, transcendence
Avoidance sounds like:
abating, abetting, abiding, abutting, aviation's, avoiding