Best way to securely store passwords for local use?

I am writing a Java application who needs three username/password pairs. I would like to add a "remember me" feature, implying I would have to store passwords on the user's computer.

Knowing this application will be used everyday by some co-workers on their own machines, I considered storing the passwords on a local encrypted file and ask for a master password who would permit to use the 3 encrypted passwords.

However, I know that password-based encryption cannot be secured if the user chooses a poor password. What could be my alternatives?