If you want, you can "lock" Kody in your town by creating another character and talking to villagers (or Kody himself) until they ask you to deliver something to another villager. Then you deliver the item, but don't return to the original villager and let them know that you did so.
For example, pretend you have both Tabby and Kody in your town. Tabby asks you to deliver a letter to Kody. Accept, and deliver the letter. Kody will ask you to thank Tabby for him. Never return to her and tell her that you delivered it. As long as you refrain from letting Tabby know you delivered the letter, both Tabby and Kody will be "locked" and unable to move.
This would also work if Kody asked you to deliver something to Tabby; it serves the same purpose, it locks them both.
I suggest doing this on a character other than your main because it's easy to talk to the first villager for a normal conversation and accidentally choose the "I delivered it!" option, which breaks the lock. If it's on a character you don't really play, you don't have to worry about it. Since it locks two characters at once you probably want to try to do this with Kody and another villager you always want in your town.
I used this method to lock Biskit and Cyrano in my town, as well as Rosie and Dotty.
Hope this was helpful to you.
