select from_unixtime(
       unix_timestamp('2008-01-01 01:00:00')+floor(rand()*31536000)
);

http://blog.underdog-projects.net/2008/10/generate-random-timestamps-in-mysql/

For me I wanted a value between 2008 and 2009 (one year: 60 seconds * 60 minutes * 24 hours * 365 days = 31536000). Because the Unix timestamp doesn’t support fractions your need to round the value to an int. (floor or round the value).

Generate Random Date in Mysql

MySQL