I want to create a desktop application that uses a relational database (such as postgres - let\'s say my best case scenario is to use postgres in this application).
I wa
Short version, you really can't, your best bet is to use SQLite or similar.
Long version, well, if you really really want to, you can create multiple unattended installers for your database that targets each platform you want, embed it into your application and install it on the first run.
Now that is just ugly and most users (myself included) would outright never use it.
You can always mention that your software depends on X and Y and provide information about how to manually install the dependencies.