General synonyms:
* Celestial
* Godly
* Holy
* Sacred
* Spiritual
* Supernatural
* Transcendent
Synonyms emphasizing beauty or excellence:
* Exquisite
* Magnificent
* Marvelous
* Sublime
* Wonderful
Synonyms emphasizing power or authority:
* Omnipotent
* Supreme
* Ultimate
Synonyms emphasizing inspiration or guidance:
* Inspired
* Prophetic
* Revealed
Synonyms emphasizing the feeling of awe or wonder:
* Awesome
* Ethereal
* Heavenly
* Mystical
More specific synonyms:
* Angelic: emphasizing the connection to angels
* Deific: emphasizing the nature of a god
* Olympian: emphasizing the connection to Greek gods
* Theological: emphasizing religious study and doctrine
The best synonym for "divine" will depend on the specific context and the nuances of meaning you wish to convey.