Here's what rhymes with unenviable.

Consider these alternatives

enviable / unenviable herculean / cerulean task / ask chore / or undeserved / first insurmountable / accountable unaccustomed / husband unassailable / available precarious / various sobriquet / they unappetizing / rising inscribes / rights ingratiated / dated unpalatable / charitable righted / ibid unrewarding / according unpleasant / present