Can Jenkins schedule builds using different time zones?

Looks like they added this in 2.60.2.

As Michael mentioned in his answer, this functionality was added. Here's an example:

TZ=Europe/Kiev
0 1 * * 5

That would run at 1:00 AM Ukraine time, once a week on Friday.

To get the names of time zones to use, you can use the column marked "TZ database name" in https://en.wikipedia.org/wiki/List_of_tz_database_time_zones