You can place you cronjob in /etc/cron.daily/ and it will automatically run in that timeframe.

Edit:

Sorry, I was referencing an old Debian installation where anacron wasn't installed by default. In that case /etc/cron.daily/ was executed by /etc/crontab on 6:25. But newer Debian installations (and so does Ubuntu) install anacron by default and so /etc/cron.daily/ will be executed by /etc/anacrontab five minutes after anacron was started or every new day.

To achieve your schedule (from the comments) you can set up a cronjob that will e.g. every 10 min between 3-6 start either anacron that will take care that the backup job only run once or you can write a custom controll script.

1. Alternative: anacron

mkdir ~/.local/share/anacron_spool

echo "1 0 backup.daily /path/to/backup.sh" > ~/.config/anacrontab

(crontab -l; echo "*/10 3-6 * * * /usr/sbin/anacron -s -t $HOME/.config/anacrontab -S $HOME/.local/share/anacron_spool") | crontab -

This will make anacron to serialize (-s) run all jobs defined in ~/.config/anacrontab. Because by default only root has write permission to write to /var/spool/anacron/ where the timestamps are stored we use a custom spool-dir (-S). If all jobs are done for today anacron will exit.

2. Alternative: custom controll script

Open an editor (e.g. sudo nano /usr/local/bin/run_once_a_day.sh) and paste this:

#!/bin/bash

SPOOL="$HOME/.local/share/run_once_spool/"

if [ $# != 2 ]; then

    echo "Usage: $(basename $0) <job-identifier> <command>"

    exit 1

fi



if [ ! -d $SPOOL ]; then

    mkdir $SPOOL

fi



if [ -e ${SPOOL}${1} ]; then

    last_run=$(cat ${SPOOL}${1})

else

    last_run=0

fi



today=$(date +%Y%m%d)

if [ $last_run != $today ]; then

    $2

    echo $today > ${SPOOL}${1}

fi

Press CTRL+O to save and CTRL+X to exit. Make it executeable and add a cronjob that will start it periodicaly with:

sudo chmod 755 !$

(crontab -l; echo "*/10 3-6 * * * /usr/local/bin/run_once_a_day.sh backup.daily /path/to/backup.sh") | crontab -