What is the best practice for securely storing passwords in Java

You can use a local keystore where you could put passwords instead of secret keys.

Answer to edit:

Keystores are a perfect fit for your need. If you want extra protection, you could ask the user for one password to access all passwords when the user starts the application. Then, you could protect stored database password with a simple salt-and-stretch method (to generate an encryption key) using the one password that was used when starting the application.

There is no way to store something on a computer in a way that your Java program can retrieve it (without the user entering some password), but no other program (running in the same user's account) on this computer can retrieve it.

You can try to encrypt it somehow and hide the decryption algorithm together with the decryption key in your program (white-box cryptography), but then the attacker just needs to run your program in a debugger to let it decrypt the data.

You could use the system's permission system, but this will usually not help if the attacker is some program running in the same user account as your Java program (and would help even less if the attacker has root access).

The best bet would be to store the password on a USB memory and tell the user to take it out when you are done using it, but if the attacking program is running and observing while you are reading the secret from the stick, even this does not help.