Telling the truth sarcastically

Is there a term for saying something in a sarcastic manner but you actually mean what you're saying?

All the time I say things sarcastically even though I mean what I say. Or if I want to tell the truth but I know no one will believe me I say it sarcastically even though what I'm saying is true. For example, everyone thinks I kissed my friend but I didn't. So when asked I reply sarcastically, "No I never kissed her", insinuating that I did because of the sarcasm in the response. But in reality I'm telling the truth that I didn't. It's almost like a false sarcasm?

See Grice's classic paper "Logic and Conversation" for the general framework employed.

When you speak with a sarcastic or singsong voice you are flouting the maxim of manner ("avoid obscurity of expression"). When you flout a conversational maxim, and you are assumed to be a cooperative conversation partner, it is assumed that you are trying to communicate something other than the literal meaning of your words (viz., it is preposterous for you to think that I would have ever kissed her) in an indirect way (perhaps it would be impolite for you to angrily deny the charge). Of course, this is the wrong inference, but unless people knew this habit of yours they couldn't help but making it.

In such a case you are taking advantage of the fact that the meaning that you cause people to falsely believe is deniable, so you are being deceptive. If on the other hand you are with your friends who know this habit of yours, and they are not deceived, then it is just that your circle has a rather ornate and perhaps exclusive way of calculating conversational implicatures.

It sounds like you are being "coy", as in definition #2:

Coy   /koi/ Adjective

(2) Reluctant to give details, esp. about something regarded as sensitive.