The Collaborative International Dictionary of English v.0.48:

Unaspiring \Unaspiring\
   See aspiring.

Moby Thesaurus II by Grady Ward, 1.0:

22 Moby Thesaurus words for "unaspiring":
   desireless, humble, inappetent, loveless, meek, modest, nirvanic,
   passionless, unambitious, unassuming, unattracted, unboastful,
   undesirous, uneager, unenthusiastic, unimposing, unobtrusive,
   unostentatious, unpresuming, unpresumptuous, unpretending,
   unpretentious