Can I assign this shipping date module to a shipping method?

Yes, you can assign this delivery date feature to any shipping method, thus you can allow customers to choose delivery date and time if they select only particular shipping method/methods.

To configure that please navigate to System > Configuration > Delivery Date > Delivery Date/Delivery Time/Comments Field and set to `Yes` the `Show For Selected Shipping Methods Only` field. Once you do that, there will be an opportunity to select needed methods in the `Shipping Methods` field:

Magento Delivery Date extension by Amasty

See more details on Delivery Date page
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