Seems like cutting a cone would be done more easily on a lathe. If you don't have a lathe, you could "make" one. Mount your piece to a power drill and mount that to your table. Start it turning. Now run your router down the piece while going a little deeper at each step.
I guess, depending on the material, you could also mount the piece in your router spindle, and move it against a stationary cutter mounted on the table.
As for doing it on the router table with no other tools... Hmmm... If the accuracy of your table is high enough, you could start with a 0-radius circle at a dept of 0, a 1-radius circle at a dept of one unit, a bigger circle at a deeper depth, etc... Until you reach the bottom.
You could also use a V-shaped router bit and do the same ideal. You wouldn't have to make as many different layers if the cone's angles were the same as the v-cutter's angle.
Finally (this one came to me last but I like it best), mount your workpiece on a rotating spindle and mount that at an angle to the router's table. Get it turning and move your router's spindle back and forth until you have a cone. With this one, you only have to work about one dimension after you get the piece mounted at the angle you want for the cone.
Then again, what do I know. I'm just a math teacher.