You can easily suppress the output of any cronjob by redirecting output to /dev/null. You can do this by appending >/dev/null 2>&1 to cronjob, for which you want to suppress output.
0 2 * * * /home/backup.sh >/dev/null 2>&1
The >/dev/null tells the cron to send all output (STDOUT) to /dev/null
The 2>@1 tells the cron to send all errors (STDERR) to same as (STDOUT)
