"Don't have a conniption" is another way of saying, "Take it easy. Don't throw a fit." Conniptions are fits or tantrums. A screaming toddler is a perfect example of a conniption, but adults who lose their tempers have conniptions too. People have conniptions when they lose their cool and can't control themselves. If you’ve been waiting in line for two hours then someone jumps ahead and takes the last cupcake, go ahead and have a conniption.