Since you are new google the # for airbnb and give them a call. It's worth it to wait on the phone. The "mistake" you may have made was canceling. In general, hosts should avoid being the ones to hit the cancel button because the system automatically blocks those dates so you can't rent them out to anyone else. The guest may have seen this cancellation and thought it was too much to bother with.
So, in general, just start with sending a message and ask them first how they would like to proceed. "Hey Mary, x important thing has come up but my neighbor Sally (here's her airbnb profile, or here's her facebook profile, i.e. she's not a murderer or anything) is willing to offer her space and it is more than comparable to mine. She has offered to take x payment (and this is where things could get weird, because people may not want to pay a stranger out of their pocketbook - they may want the protection of airbnb so if Sally doesn't have an airbnb listing, that may be why they aren't accepting).
If the guest writes back and says "that is terrible no thanks" then from there you can work out the cancellation business, or offer to keep the accomodation in place, but any time you are the one to cancel it gets blocked on your calendar so you can't book anyone else during that time.
