You don't happen to have an AV cable that can plug into the
MULTI OUT port, do you?
I think even N64 and GameCube MULTI OUT cables are compatible with the SNES, so if you have either of those consoles, you might be in luck.
If you don't have a spare MULTI OUT AV cable, you might have to try plugging the RF cable in where the TV's antenna cable goes (plug the antenna cable into the RF cable so that you can still watch TV when the SNES is off), and see how you go tuning in an unused channel to the SNES frequency. I had to use this technique to set up a SNES on a flat screen TV for a friend of mine a month ago, and it was an absolute pain; eventually I worked out that I had to change the channel's "mode", and I'm not even sure now what "mode" I changed, or what I changed it from/to... but if you need, I could probably find out the details for you.
Hopefully you don't have to use the RF technique, or it's easier to do on your TV...
Good luck!