Confidence can mean either trust or hope. If you mean trust, the antonyms are unbelief, disbelief, incredulity, doubt, uncertainty, skepticism, misgiving, demur, discredit, distrust, mistrust, suspicion, jealousy, scruple, qualms. If you mean hope, the antonyms are hopelessness, despair, desperation, despondency, dejection, pessimism, dashed hopes, abandon all hope, give up, give over, falter, hopeless, forlorn, inconsolable, undone, irreparable. source: Roget's Thesaurus

The antonyms (opposites) are actually diffident and diffidence. Note the -fid- root. Still, some speakers add "un-", especially to create "unconfident". The other problem is that "confidence" has a couple of meanings. "Inconfidence" is actually possible, but it has nothing to do with being sure.

opposite of confident . unsure It should be 'unconfident'. Uncertain, unsure... oposite of confidence. 1 Timidity 2 Doubt