There are two options open to you in this scenario:
a) Use another service
b) Sign your client up to Open Table (with their permission)
In investigating the business needs of your client before you began work on the app you would have noted if they were on another table reservation service online (such as UrbanSpoon) and in that case the former approach works fine.
If they are not, then we recommend that YOU recommend they take advantage of the service in order to get the feature into their app.