Wix apps are proprietary, thus the only control you have over them is what they give you.
So if there is no built-in functionality that suit your needs, you can create your custom payment flow and integrate a Date Picker element in it.
Corvid: Formatting Dates
Corvid Tutorial: Processing Payments
There are some related forum posts that might help you start:
Wishlist Page is the new official platform for requesting new features. You can vote, comment, and track the status of the requested features (requests from this page will be migrated to the new Wishlist soon).