The wiring is what is going to be at issue here as you likely have speaker wire run to your wall plate which is not the 75 ohm cable that should be used to send out your subwoofer audio.
So, if you have zero ability to retro in a piece of coax, then almost any conversion will provide decent results. I would look for a couple of RCA wall plates online and then terminate the back side of them to the cable in the wall. This will still leave you open to some interference and hum on your sub though since the cable is not correct.
Good luck though - it is a gamble when in this situation, and sometimes you win.
EDIT: This is a link to a RCA connector that has solder on connections on the back. You can replace your banana connectors with this type of RCA plate and solder for a secure connection point.
http://www.hubbellpremisewiring.com/...551N4&PID=1218