As you have discovered yourself, there is no standard attribute to store a timezone associated with a user. This is not an OpenDJ only issue, it's an LDAP-wide standard issue. The only one that I know of is attached to NIS+ schema and I'm not even sure it's defined as being generic enough. The proper way to do this would be to define a new attribute and an auxiliary objectclass to contain that attribute. With OpenDJ, you could also define an "ENUM" syntax to restrict the values to proper timezones.
You could for your own application decide to "abuse" another attribute to store the timezone. But this may create confusion to other applications that will connect to the server in the future. I would not recommend it.
Kind regards, Ludovic