Conversate, formed by backformation from the noun conversation, appears in a few dictionaries, but it always bears replacement with the shorter converse. If you need a verb corresponding to conversation but converse doesn’t sound right, there are plenty of perfectly good synonyms, such as talk, chat, speak, discourse, discuss, and confer.
Conversate appears most often in speech, and all the examples we could find on the web come from transcriptions of quoted speech—for example:
He would bake breads at the house and things and would conversate about foods. [transcribed in Wichita Eagle]
Unfortunately we rarely get the time to conversate much beforehand. [transcribed in Pro Fighting Fans]
Me and Coach Belichick, it’s more a mental bond. We don’t really conversate. [quoted in Sports Illustrated]
Ed Orgeron basically had conversated with my ex-head coach … [quoted in Yahoo! Sports]