I doubt that there is a coax adapter that will work in this setup. HDMI-ARC uses a different set of pins for the audio that AMP expects over its HDMI connection. The coax adapters that I’ve seen send from a source to the TV. With HDMI-ARC the TV can send audio from TV Apps, back to an A/V receiver or to AMP. There is also a CEC (Consumer Electronics Control) two way channel in the HDMI connection that the coax adaptor will not support. AMP expects a working CEC connection and uses this to setup HDMI-ARC service from the TV.

There are a couple work arounds. You could use an audio extractor in the HDMI connection from AppleTV. The extractor should have an optical output that can be sent to AMP through a ‘dongle’ that is available from SONOS. This optical connection does not support super advanced audio, but this is not a big deal because AMP supports 4.1. You would set AppleTV to use Dolby Digital.5.1 (AMP will convert this to 4.1). A much more expensive arrangement would be Arcana. I’m using Arcana with my SONOS ARC and a TV that does not offer HDMI-ARC.

Thank you for the reply. For clarification, I do not wish to use Apple TV, the new tv has google TV built in. I referenced my old setup with Apple TV sending signal over coax via transmitter at the Apple and receiver at the tv to show that the setup worked for Apple TV. 
I moved the transmitter adapter to the tv and the receiver in front of the amp hoping it would work. 
I questioned the arc as well. I assumed the hdmi arc signal would be too complex for a hdmi converter. 
Is the extractor you are referring to remote? So far I can not find a digital audio device that transfers signal over traditional rg59 coax. I have an optical audio output on the tv. Thought about trying an optical to hdmi dongle then using the HDMI’s to coax converter. Thoughts?

I need hdmi arc from tv over BNC to the amp.

I think that your best bet would be to convert the TV’s optical output to coax and use AMP’s analog input. At the AMP end of the coax transmission plan on using an isolation transformer, but you could accidentally get very lucky and not need one. You’ll not have CEC control of AMP, but you can set AMP to sense audio input and turn ON.

Volume control of AMP using IR may be a challenge. With a quickie search I did not find an integrated optical (TOSLINK) to coax converter that could embed IR control for AMP. over the coax.

I have made some adjustments, setup below works with my old AVR.

Optical out from tv → optical/coax splitter→ bnc cable to av cabinet->bnc cable plugged into coaxial audio input on AVR.

I used F-type female to RCA male adapters on both ends of the bnc cable that runs in wall from tv to media cabinet.

When I plug the bnc into the red/white audio input on AVR it doesn’t work.

Neither the Sonos or AVR will work when audio from tv is plugged into the red/white audio in. I am only able to push audio from tv over bnc when I input to AVR via coaxial. 
Conclusion, I don’t think it’s possible to send audio over bnc to Sonos amp.

The signal running over coax to the receiver is still digital at the receiver end. If you want a L/R signal, you’ll need a TOSLINK to analog audio converter.

Yep, I had a moment, my brain worked, and realized the same right after I typed my comment. LOL.
I purchased an insignia digital to analog converter and everything works.

currently trying to figure out how to control volume. I have a harmony remote, may use that. Thank you for your responses!

Just claim to Harmony that you are controlling an A/V receiver or TV with IR. The model is arbitrary, but I recommend not using something nearby. Then you can train AMP to use these codes.

Good idea!