I believe there are two ways you can delete your club penguin account.
1. Don't use your account for 90 days (3 months to be frank), and CP will by and by delete your account automatically.
2. Somehow email CP that you want to delete your penguin. You might get a response from CP saying something along the lines of "Are you sure?" Say yes, and HOPEFULLY CP will delete your account for you.
Hope this helps! :)