How can I run voice over existing coaxial cable?
Assuming you don't already have ethernet available in the garage, you COULD use a pair of MoCA adapters to use the coax for ethernet.

Beyond that, the two magic terms you'll need to Google for are "FXO" and "FXS". A FXO VoIP gateway is basically a VoIP server that's connected to a telephone line. A FXS VoIP interface is basically a VoIP client that uses a regular telephone as its input and output device. In theory, any device capable of being a FXO server should be able to be a FXS client as well, because the interface hardware is basically the same... but if you can find a FXS adapter, it'll probably be cheaper than buying two FXO servers.

Don't take my word for it without further research (it's been about 10 years since I last looked into it), but I think at least one member of the Linksys SPA-3xxx family can be used for this purpose if you buy a pair of them... basically, each box has an ethernet port, a FXO jack, and a FXS jack. You'd configure one of them as a FXO gateway and VoIP server with local LAN IP address &amp; connect its FXO jack to the phone jack, and configure the other one as a FXS client that connects to the first &amp; plug the phone into its FXS jack.

Be careful with the SPA-3xxx (and SPA-21xx?) devices, though... some of them are service-locked, especially if you buy one that isn't brand new. From what I remember, the only way to know for sure whether it's locked to a specific service is to try accessing its configuration menu... if it's locked, you won't be allowed to change the SIP or FXO settings. Also, there are two passwords... one of which is necessary for "advanced" settings and can NOT be factory reset. I remember reading about how a bunch of people who bought cheap ones on eBay to use with Asterisk &amp; discovered that they were basically paperweights due to service locks or lost passwords.