Use the adverb conceivably when you're talking about something that is believable or possible. You could say, for example, that you'll conceivably still be on time to work after oversleeping, especially if you skip breakfast.
You might tell your sister that you could conceivably go on every single ride at the state fair in an hour, if you move quickly and don't stop to eat fried dough. You could also say that your favorite baseball team might conceivably win the World Series next year. Conceivably comes from its adjective form, conceivable, and both words are rooted in the Latin concipere, which means "take in, hold, or grasp" and also "become pregnant."