I will try to think of what I would do --lay the dog on my two legs, head down , on it side , and give a good sound slap on the back to dislodge the stuck item.. lay it on its side, head touching your feet.at your feet! hold your hand under its hold it high to your legs, and whack its back--that are laying on your legs(((( much like holding your child by it legs , and slapping it back) gravity should dislodge the item !!
or try this method, stretch the dog over the back of a chair , tummy side down . and give a good slap to the back right about the chest area!! this way will be easier to achieve, with the dog laying down over the chair on its tummy !! this is similar to doing a self Heimlich to ones self!