Right, there is no Ethernet WIC that will work in the 2600. The WIC-1ENET is for 17xx only. There's some new HWIC ethernet modules only for the 1800/2800/3800 models.
Well, you don't have a FastE now, just a single 10. There's two solutions. The NM-1E to get you one 10-Base-T port. Or the NM-16ESW to get you a 10/100 port with a 16-port Switch attached.
If you don't need the token ring port on your router now, it may be easier/quicker/cheaper to just buy a new 2801/2811 that will come with dual FastE's if that is what you want.