This would work.
First router
192.168.0.1
255.255.255.0
DHCP range - 192.168.0.100-200
Second router
192.168.0.2
255.255.255.0
Gateway 192.168.0.1
DNS 192.168.0.1
DHCP disabled
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To configure the second router, I would connect a laptop or PC directly to it (no other cables), go to the config page (probably 192.168.0.1 or 192.168.1.1)
Then..
Step one
disable DHCP
Now set a static IP on your laptop of 192.168.0.3 (assuming the IP of the device is 192.168.0.1)
Check that you can ping the IP of the second router (192.168.0.1) -whilst still directly connected to it.
Now set the IP of that second router to 192.168.0.2, wait for it to restart (if it does), then ping that IP from the laptop.
Set the DNS and gateway as my suggested settings above.
Disconnect the laptop and remove the static IP from the laptop.
Connect the second router up to the first using a switch port (not WAN port on router), then see if you can ping both routers when connecting the laptop up to both of them (using auto-IP assignment on the laptop)