Formal:
* "Bene vale!" This literally means "fare well!" and is a polite way to say goodbye.
* "Sit tibi dies felix!" This means "May you have a fortunate day!"
* "Dies tibi laetus sit!" This means "May your day be joyful!"
Informal:
* "Bonam diem!" This is a straightforward "good day!"
* "Dies tibi gratus sit!" This means "May your day be pleasant!"
More specific:
* "Vale, et fortunam habe!" This means "Farewell, and have good luck!"
Important note: Latin was a spoken language, and formal phrases were common in writing. For casual, everyday use, people likely used more informal, everyday greetings.