You can use emoji as stamps by registering them as templates. This is surprisingly handy, so please give it a try. Here is how.
- Touch and hold a date on the calendar, open "Templates", and tap "Add a Template"
- Set just an emoji as the event title and save it. If it doesn't need a time, making it an all-day event works well (if the label showing up on the calendar bothers you, set a suitable time instead)
- Touch and hold the date where you want the stamp, open "Templates", and tap the stamp to add it
From then on, you can use it just like a stamp.