Change the time zone of a cronjob

This will likely depend on your OS and it's implementation of cron. This is not possible in the most popular cron implementation, vixie/isc cron. From the crontab(5) manpage:

LIMITATIONS
       The  cron  daemon  runs with a defined timezone. It currently does not 
       support per-user timezones. All the tasks: system's and user's will 
       be run based on the configured timezone. Even if a user specifies  
       the TZ  environment  variable  in  his crontab this will affect only 
       the commands executed in the crontab, not the execution of the crontab 
       tasks themselves.

Expanding on @Cyrus answer this is what I did:

I made a script which checked a UTC offset:

#!/bin/bash
export TZ=":US/Eastern"
if [ "$(date +%z)" == "$1" ]; then
  shift
  exec $@
fi

Then I add two crontab entries each for the offset I want:

0 8 * * * run-only-with-tz.sh -0400 place_your_command_here
0 9 * * * run-only-with-tz.sh -0500 place_your_command_here

Move your cronjob to 8:00 and sleep one hour if you are in GMT+1

0 8 * * * [ "$(date +\%z)" = "+0100" ] && sleep 3600; place_your_command_here