Router has no coax connector. Need to connect Spectrum internet to my R8000P X6S

> How to connect acoax cable to router that has no cable connector.

   You don't; you connect it to a cable modem.

> My current older Netgear C3700 has a coax cable internet connector on
> it.

   C3700[v1] or C3700v2?  Look for "Model" on the product label.

   If the modem section of your C3700[vX] satisfies your modem
requirements, then you should be able to disable its router, and use it
as your modem.

   Visit http://netgear.com/support , put in your (actual) model number,
and look for Documentation.  Get the User Manual (at least).  Read.
Look for "Cable Your Modem Router to a Router or Gateway".

   You might want to check with your ISP to see if they support that
modem(+router) at the Internet speed you've subscribed to.