You can be both honest and give yourself some leeway with offering to be there by a certain date as mentioned above.
You might offer, if YOU have any interest, in providing premium/preferred type of service (usually OT for you) but it would definitely have to come with a premium pricetag.
Other than that, you can offer any cancellation or delay-caused spots to them at regular rates while scheduling them in your next available time.
The good/bad news is that it might indicate you need more help.
