If your original ID isn't banned, You can get ITA Manager (I know you don't want too), or you can get CFW Setup V4, Along with many other homebrew apps to restore your IDPS before signing in. All you need to do on CFW Setup V4 is Load up the homebrew app, It'll ask if you want to restore you IDPS, click yes, then quit the application. From there select your game, wipe your history and enjoy signing in online.
If your CID is banned, you can use CCAPI to change your IDPS before you sign in, which there are many tutorials on how to do this. Post above me pretty much states all you have to do.