sob out
To attempt to say something while in the middle of sobbing. A noun or pronoun can be used between "sob" and "out." After getting caught stealing, the poor child sobbed out a pitiful story about how he couldn't afford to pay for the food. He sobbed an apology out, promising to never do it again.
sob something out
to speak something out while sobbing. Wally sobbed his story out while the police made notes. He sobbed out his sad tale.