Please actually read why the game was disabled in the first place.

CoD: World at War doesn't work because they were on NWFC but CoD: Modern Warfare Reflex, CoD: Black Ops, and CoD: Modern Warfare 3 are still online in 2016. I recommend if you want to find players to play with type in "CoD: Modern Warfare 3 wii online 2016" for example and some YouTube videos from this year should come up. It'll be hard to find players but they're out there! Good Luck!

Take a look at this.
CTRL+F 'Call of Duty'

There is only one entry, which is disabled. The rest haven't been tested or anything yet, hence why it doesn't work at all with use for Wiimmfi.
The game(s) need to be tested and where possible properly patched before you're able to connect to Wiimmfi from these games.
If you want to test, or help testing you can contact Wiimm (or other Wiimmfi moderators if applicable). This requires you to have some more technical knowledge over networking, such as being able to packet sniff from your Wii console.

Edit: Seems like the other existing CoD games have their servers run at Activision, and therefore should be able to work the regular method. If you have troubles connecting, consider checking your Internet settings, or contact Activision for assistance.

This is not WIimmfi-related, I suggest a moderator to move this topic to an appropriate forum board.