Immobility rhymes with:
accessibility, advisability, believability, collectibility, comparability, convertibility, credibility, culpability, deniability, dependability, desirability, disability, durability, eligibility, enforceability, fallibility, favorability, flammability, gullibility, impossibility, inability, incompatibility, indestructibility, inevitability, infallibility, inflexibility, instability, invincibility, invulnerability, liability, maneuverability, marketability, miscibility, permeability, plausibility, portability, predictability, profitability, readability, respectability, sensibility, stability, suitability, survivability, sustainability, taxability, transferability, unavailability, unbreakability, unpredictability, unprofitability, unreliability, variability, visibility, vulnerability
Immobility sounds like:
impaled, impelled, implied, implode, imploded, impolite, inability, infield, inflate, inflated, invalid, invalidate, invalidated, inviolate