To use the DS3231 RTC first add "i2c0" to overlays= in /boot/dietpiEnv.txt without quotes and separated by a space, for example:

overlays=usbhost2 usbhost3 i2c0

 Create a systemd service to sync the system time automatically during the boot process. Create /etc/systemd/system/add-rtc.service and add the following:

[Unit]
Description=Sync system time to RTC
Requires=sysinit.target

[Service]
Type=oneshot
ExecStart=/usr/bin/bash -c 'echo ds1307 0x68 > /sys/class/i2c-adapter/i2c-0/new_device'
ExecStart=/bin/sleep 2
ExecStart=/sbin/hwclock -f /dev/rtc1 -s

[Install]
WantedBy=sysinit.target

 Enable the service:

sudo systemctl daemon-reload
sudo systemctl enable add-rtc

 Use dietpi-config to disable the fake hardware clock and set time synchronization to custom.