I wrestled with this problem and implemented the 'convertToNull' solutions discussed above. It worked in my local MySql instance. But when I deployed my Play/Scala app to Heroku it no longer would work. Heroku also concatenates several args to the DB URL that they provide users, and this solution, because of Heroku's use concatenation of "?" before their own set of args, will not work. However I found a different solution which seems to work equally well.
SET sql_mode = 'NO_ZERO_DATE';
I put this in my table descriptions and it solved the problem of '0000-00-00 00:00:00' can not be represented as java.sql.Timestamp