Common words:
* Daybreak
* Daydream
* Daylight
* Daytime
* Daybook
* Daycare
* Daytrip
Less common words:
* Daystar (a poetic term for the sun)
* Dayflower (a type of plant)
* Dayfly (a type of insect)
* Daywork (work done during the day)
* Daysman (an arbitrator or mediator)
Do you have a specific category in mind for your compound word? That would help me give you a more tailored answer!