Here's what rhymes with ineligible.

Consider these alternatives

eligible / intelligible eligibility / stability disqualified / side disqualify / high deemed / seemed qualify / high unfit / which excluded / included automatically / dramatically barred / part unsuitable / suitable ineligibility / stability qualified / side qualifies / size unconstitutional / constitutional unavailable / available void / avoid nullified / side enroll / whole citizenship / which disqualifying / dying moot / food apply / dry obligated / dated