Call in and say you're having some problems with your stomach. Oftentimes, "problems with the stomach" implies diarrhea. This is enough to deter most bosses from denying your sick day request. After all, if you'll be running to the bathroom every hour, and presumably, spending some time there, so it's not like you'll be productive. Even more so, an illness like that might even make your boss encourage you to stay home. Obviously, don't use the word "diarrhea" in your request; simply saying "problem with my stomach" implies it in most cases. In the end, you'll get to enjoy two days off in a row.
When you return to work, act like nothing is wrong, and don't bring anything up. If your boss asks you about your illness, say something like: "I'm not sure, but I think ordering my burger rare was a mistake [implying that you ate at a restaurant during the last few days]". This provides an obvious, even slightly humorous, explanation to your stomach problems, and makes your story sound truthful. It's not too uncommon to get stomach problems from eating undercooked meat, so people will understand. Having given your answer, proceed with your usual day as normal.