General antonyms:
* Insincere
* Dishonest
* Deceitful
* Fake
* Artificial
* Superficial
* Untruthful
* Hypocritical
More specific antonyms:
* Pretentious (for a person who is insincere in their attempts to impress)
* Calculating (for someone who is insincere in their motives)
* Manipulative (for someone who is insincere in their attempts to control others)
* Cynical (for someone who is skeptical and distrustful of sincerity)
The best antonym for "sincere" will depend on the specific context in which the word is being used.