Facility rhymes with:
accessibility, advisability, believability, collectibility, comparability, convertibility, credibility, culpability, deniability, dependability, desirability, disability, durability, eligibility, enforceability, fallibility, favorability, flammability, gentility, gullibility, humility, immobility, impossibility, inability, incivility, incompatibility, indestructibility, inevitability, infallibility, infertility, inflexibility, instability, invincibility, invulnerability, liability, maneuverability, marketability, miscibility, motility, nonutility, permeability, plausibility, portability, predictability, profitability, readability, respectability, sensibility, stability, sterility, suitability, survivability, sustainability, taxability, tranquility, transferability, unavailability, unbreakability, unpredictability, unprofitability, unreliability, variability, visibility, vulnerability
Facility sounds like:
facilitate, facilitated, faculty, fizzled, fjeld, fusillade