Wordnet 3.0
ADJECTIVE (2)
1. 
 hard to deal with; 
 especially causing pain or embarrassment; 
- Example: "awkward (or embarrassing or difficult) moments in the discussion"- Example: "an awkward pause followed his remark"- Example: "a sticky question"- Example: "in the unenviable position of resorting to an act he had planned to save for the climax of the campaign"[syn: awkward, embarrassing, sticky, unenviable]
2.  so undesirable as to be incapable of arousing envy; 
- Example: "unenviable notoriety"
The Collaborative International Dictionary of English v.0.48:
Unenviable \Unenviable\
   See enviable.
WordNet (r) 3.0 (2006):
unenviable
    adj 1: hard to deal with; especially causing pain or
           embarrassment; "awkward (or embarrassing or difficult)
           moments in the discussion"; "an awkward pause followed
           his remark"; "a sticky question"; "in the unenviable
           position of resorting to an act he had planned to save
           for the climax of the campaign" [syn: awkward,
           embarrassing, sticky, unenviable]
    2: so undesirable as to be incapable of arousing envy;
       "unenviable notoriety"