First off, make sure you're using your Disney account username and not your penguin name. You can check this article for help:
If you still can't login to your account:
1. Choose either username or password on the line that says 'Forgot username of Password.'
2. Enter your account's parent email address and tap Continue. An email will be sent to that address.
Has an email from Disney Account Member Services not arrived after 15 minutes? No problem! It might have ended up in your parent's junk mail folder, so remind them to check there too.
3. In the email, tap on Recover Disney Account to open the account manager. A window will open with a list of your Disney Account usernames.
4. Click on the down arrow next to an account if you want to change the username or password.
5. Enter a new username or password.
6. Log into Club Penguin Island with the username and password you've created.
Welcome back to the island!