@Paul7319 You mean a credit for a future stay with you? If so, you can just do it manually: if they choose to book again, either send them a special offer for the stay for the reduced amount, or offer to send them money using the Resolution Center at the end of their stay. There is no way to do it automatically or to issue a voucher.
@Bob297 You could also do that, I guess... I would personally prefer that they have a reservation through Airbnb so that everything is aboveboard and traceable and you can write them a review at the end of their stay. Also, you wouldn't have any protection through Aibrnb if you don't do a proper reservation (for whatever that's worth). But it's your listing and you can administer it however works best for you.