In a nutshell:
No usable constructor for java.time.ZonedDateTime
Can't find a codec for class java.time.LocalDateTime
I pushed support for the more common Java 8 datetime types to Morphia last week targeting the 1.3 release. See the issue here and the linked commits. If there's a type you need that's not listed, please file a Morphia issue and I'll try to make sure it's included in 1.3 as well.