How can I use SIRI on my iPhone or iPad to create appointments in Daylite?

To be able to do this, working from Daylite on Mac, you must set up Calendar Sharing via CalDAV. To begin with, do the following:

Choose Daylite > Settings.
Click Calendar Sharing.
Select the "In Other Apps" tab.
Select whether you wish to share Daylite calendar as "One calendar" or use "Separate calendars for each category."

Now create a CalDAV account for Daylite in the Calendar app.

The next step is to set up Daylite calendar as your default calendar on the iPhone or iPad.

To do this,

Tap Apple Settings.
Go to Calendars.
Select Default Calendar and set it to "Daylite Calendar."

Once done, create appointments in the Calendar app on your iPhone or iPad using Siri. Those appointments will be available in Daylite on Mac under My Calendar after the next sync.

If you are unable to choose Daylite as your default Calendar and only see Category-specific Calendars, then you will need to change your Daylite Preferences. From Daylite’s Menu Bar > Daylite > Preferences > Calendar Integration > Daylite Calendar in Other Apps, here you will need to change the Show Appointment as "One Calendar". You can then proceed with the steps to make your Daylite Calendar your default Calendar on your device.