I'm not exactly clear what it is you want to accomplish, but if I understand correctly that you want to have an Ethernet connection for a single device in another part of your house, a part of the house where there's an existing coax feed, then a MoCA adapater should do the trick for you.
If indeed you're just trying to get that single Ethernet connection you won't need another router. You can plug the Ethernet device directly into the output of the MoCA adapter.
If you need more than one Ethernet connection after the MoCA adapter what you can use is a simple and inexpensive Ethernet switch. Again, you don't need another router.
The only case I can envision for needing a second router in your situaiton is if you want to use it to extend WiFi coverage, but just for Ethernet connection(s) a second router is not needed and may be counter productive.